Maths-

General

Easy

Question

# Find the volume of a sphere whose surface area is 154 sq.cm

Hint:

### The surface area of a sphere is

## The correct answer is: 179.67cm3

### Explanation:

- We have given surface area .
- We have to find the volume of the sphere.

Step 1 of 1:

We have given surface area 154cm^{2}.

So,

r = 3.5

Volume of sphere

Thus, the volume of the sphere is 179.67cm^{3}.

### Related Questions to study

Maths-

### A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1m , then find the volume of the iron used to make the tank ?

Explanation:

Since the hemispherical tank is made of 1cm thick iron, we can find the outer radius of the tank by adding thickness to the inner radius.

The Volume of hemisphere of base radius r is equal to

The inner radius of the tank r = 1m

Thickness of iron = 1cm = 1/100 m =0.01m

Outer radius of the tank, R = 1m + 0.01m = 1.01m

The volume of the iron used to make the tank can be calculated by subtracting the volume of the tank with inner radius from the volume of the tank with outer radius.

Volume of the iron used to make the tank

0.06348 m

- We have given a hemisphere with thickness 1cm.
- We have to find the volume of iron used to make the tank.

Since the hemispherical tank is made of 1cm thick iron, we can find the outer radius of the tank by adding thickness to the inner radius.

The Volume of hemisphere of base radius r is equal to

The inner radius of the tank r = 1m

Thickness of iron = 1cm = 1/100 m =0.01m

Outer radius of the tank, R = 1m + 0.01m = 1.01m

The volume of the iron used to make the tank can be calculated by subtracting the volume of the tank with inner radius from the volume of the tank with outer radius.

Volume of the iron used to make the tank

0.06348 m

^{3 }of iron used to make the tank### A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1m , then find the volume of the iron used to make the tank ?

Maths-General

Explanation:

Since the hemispherical tank is made of 1cm thick iron, we can find the outer radius of the tank by adding thickness to the inner radius.

The Volume of hemisphere of base radius r is equal to

The inner radius of the tank r = 1m

Thickness of iron = 1cm = 1/100 m =0.01m

Outer radius of the tank, R = 1m + 0.01m = 1.01m

The volume of the iron used to make the tank can be calculated by subtracting the volume of the tank with inner radius from the volume of the tank with outer radius.

Volume of the iron used to make the tank

0.06348 m

- We have given a hemisphere with thickness 1cm.
- We have to find the volume of iron used to make the tank.

Since the hemispherical tank is made of 1cm thick iron, we can find the outer radius of the tank by adding thickness to the inner radius.

The Volume of hemisphere of base radius r is equal to

The inner radius of the tank r = 1m

Thickness of iron = 1cm = 1/100 m =0.01m

Outer radius of the tank, R = 1m + 0.01m = 1.01m

The volume of the iron used to make the tank can be calculated by subtracting the volume of the tank with inner radius from the volume of the tank with outer radius.

Volume of the iron used to make the tank

0.06348 m

^{3 }of iron used to make the tankMaths-

### How many litres of milk can a hemispherical bowl of diameter 10.5 cm hold?

Explanation:

The diameter of the hemispherical bowl is

Radius will be

So, The volume of the hemispherical bowl will be

Also we know that

So,

- We have given a hemispherical bowl of diameter 10.5cm
- We have to find how many litre of milk this bowl can hold.

The diameter of the hemispherical bowl is

Radius will be

So, The volume of the hemispherical bowl will be

Also we know that

So,

### How many litres of milk can a hemispherical bowl of diameter 10.5 cm hold?

Maths-General

Explanation:

The diameter of the hemispherical bowl is

Radius will be

So, The volume of the hemispherical bowl will be

Also we know that

So,

- We have given a hemispherical bowl of diameter 10.5cm
- We have to find how many litre of milk this bowl can hold.

The diameter of the hemispherical bowl is

Radius will be

So, The volume of the hemispherical bowl will be

Also we know that

So,

Maths-

### of an isosceles triangle ABC is acute in which and . Prove that

Solution :-

Aim :- prove

Hint :- Using pythagoras theorem, find the length of side AB and BC .

Substitute the RHS of in terms of AC and CD Explanation(proof

Using pythagoras theorem,in triangle BDC

— Eq1

Using pythagoras theorem,in triangle BDA — Eq2

Substitute Eq2 in Eq1

Substitute AD = AC - CD (from diagram)

Hence proved

Aim :- prove

Hint :- Using pythagoras theorem, find the length of side AB and BC .

Substitute the RHS of in terms of AC and CD Explanation(proof

Using pythagoras theorem,in triangle BDC

— Eq1

Using pythagoras theorem,in triangle BDA — Eq2

Substitute Eq2 in Eq1

Substitute AD = AC - CD (from diagram)

Hence proved

### of an isosceles triangle ABC is acute in which and . Prove that

Maths-General

Solution :-

Aim :- prove

Hint :- Using pythagoras theorem, find the length of side AB and BC .

Substitute the RHS of in terms of AC and CD Explanation(proof

Using pythagoras theorem,in triangle BDC

— Eq1

Using pythagoras theorem,in triangle BDA — Eq2

Substitute Eq2 in Eq1

Substitute AD = AC - CD (from diagram)

Hence proved

Aim :- prove

Hint :- Using pythagoras theorem, find the length of side AB and BC .

Substitute the RHS of in terms of AC and CD Explanation(proof

Using pythagoras theorem,in triangle BDC

— Eq1

Using pythagoras theorem,in triangle BDA — Eq2

Substitute Eq2 in Eq1

Substitute AD = AC - CD (from diagram)

Hence proved

Maths-

### The Diameter of the moon is approximately one fourth of the diameter of the earth. What fraction of the volume of the earth is the volume of the moon?

Explanation:

Let the diameter of moon be ,Then the diameter of earth will be 4d

So, Radius of moon will be . And the radius of earth will be

Since, both earth and moon are sphere

We can use formula of volume of sphere .

And volume of earth will be

Therefore, the fraction will be

- We have given the diameter of moon is approximately one fourth of the diameter of the earth.
- We have to find the fraction of the volume of the earth is the volume of the moon

Let the diameter of moon be ,Then the diameter of earth will be 4d

So, Radius of moon will be . And the radius of earth will be

Since, both earth and moon are sphere

We can use formula of volume of sphere .

And volume of earth will be

Therefore, the fraction will be

### The Diameter of the moon is approximately one fourth of the diameter of the earth. What fraction of the volume of the earth is the volume of the moon?

Maths-General

Explanation:

Let the diameter of moon be ,Then the diameter of earth will be 4d

So, Radius of moon will be . And the radius of earth will be

Since, both earth and moon are sphere

We can use formula of volume of sphere .

And volume of earth will be

Therefore, the fraction will be

- We have given the diameter of moon is approximately one fourth of the diameter of the earth.
- We have to find the fraction of the volume of the earth is the volume of the moon

Let the diameter of moon be ,Then the diameter of earth will be 4d

So, Radius of moon will be . And the radius of earth will be

Since, both earth and moon are sphere

We can use formula of volume of sphere .

And volume of earth will be

Therefore, the fraction will be

Maths-

### The diameter of a metallic ball is 4.2 cm. What is the mass of the ball , if the density of the metal is 8.9 g per cubic cm ?

Explanation:

We will first find the volume of the metallic ball

Now we know that

Density =

Put the value of density and volume in formula, we will get mass

Density =

8.9 =

Mass = 8.9 310.399gm

= 2762.5511gm

- We have given diameter of metallic ball .and the density of the metal is
- We have to find the mass of the ball.

We will first find the volume of the metallic ball

Now we know that

Density =

Put the value of density and volume in formula, we will get mass

Density =

8.9 =

Mass = 8.9 310.399gm

= 2762.5511gm

### The diameter of a metallic ball is 4.2 cm. What is the mass of the ball , if the density of the metal is 8.9 g per cubic cm ?

Maths-General

Explanation:

We will first find the volume of the metallic ball

Now we know that

Density =

Put the value of density and volume in formula, we will get mass

Density =

8.9 =

Mass = 8.9 310.399gm

= 2762.5511gm

- We have given diameter of metallic ball .and the density of the metal is
- We have to find the mass of the ball.

We will first find the volume of the metallic ball

Now we know that

Density =

Put the value of density and volume in formula, we will get mass

Density =

8.9 =

Mass = 8.9 310.399gm

= 2762.5511gm

Maths-

### Find the amount of water displaced by a solid spherical ball of diameter 0.21m

Explanation:

We know that the volume of water displaced by the given sphere will be equal to volume of sphere.

So,

Volume of sphere will be

- We have given a solid spherical ball with diameter
- We have to find the volume of water displaced by the given sphere.

We know that the volume of water displaced by the given sphere will be equal to volume of sphere.

So,

Volume of sphere will be

### Find the amount of water displaced by a solid spherical ball of diameter 0.21m

Maths-General

Explanation:

We know that the volume of water displaced by the given sphere will be equal to volume of sphere.

So,

Volume of sphere will be

- We have given a solid spherical ball with diameter
- We have to find the volume of water displaced by the given sphere.

We know that the volume of water displaced by the given sphere will be equal to volume of sphere.

So,

Volume of sphere will be

Maths-

### Write truth table for the converse of p → q.

Hint:

If a conditional statement of the form "If p then q" is given. The converse is "If q then p." Symbolically, the converse of p q is

q p

Solution

The converse of the conditional statement p q is q p

Final Answer:

Hence, we have drawn the truth table above.

If a conditional statement of the form "If p then q" is given. The converse is "If q then p." Symbolically, the converse of p q is

q p

Solution

The converse of the conditional statement p q is q p

Final Answer:

Hence, we have drawn the truth table above.

### Write truth table for the converse of p → q.

Maths-General

Hint:

If a conditional statement of the form "If p then q" is given. The converse is "If q then p." Symbolically, the converse of p q is

q p

Solution

The converse of the conditional statement p q is q p

Final Answer:

Hence, we have drawn the truth table above.

If a conditional statement of the form "If p then q" is given. The converse is "If q then p." Symbolically, the converse of p q is

q p

Solution

The converse of the conditional statement p q is q p

Final Answer:

Hence, we have drawn the truth table above.

Maths-

### Find the volume of a sphere whose radius is 0.63 m

Explanation:

We know that the volume of sphere with radius is .

Now put the value of

So,

- We have given a sphere with radius .
- We have to find the volume of sphere.

We know that the volume of sphere with radius is .

Now put the value of

So,

### Find the volume of a sphere whose radius is 0.63 m

Maths-General

Explanation:

We know that the volume of sphere with radius is .

Now put the value of

So,

- We have given a sphere with radius .
- We have to find the volume of sphere.

We know that the volume of sphere with radius is .

Now put the value of

So,

Maths-

### Make a valid conclusion in the situation.

If two points lie in a plane, then the line containing them lies in the plane.

Points A and B lie in plane PQR.

Hint:

Law of Detachment states that if p q is true and it is given that p is true then we can conclude that q is also true. Here, the statement is termed as Hypothesis and the statement q is termed as conclusion.

Solution

Consider the statement into two separate statements

p: Two points lie in a plane

q: Line containing the two points is in the plane

So we can write the given statement “If two points lie in a plane, then the line containing them lies in the plane” as

p q

We are given that two points A and B lie in plane PQR so we can conclude that the line containing the points A and B lie in the plane PQR.

Final Answer:

Hence we can conclude that the line containing points A and B lie in the plane PQR.

Law of Detachment states that if p q is true and it is given that p is true then we can conclude that q is also true. Here, the statement is termed as Hypothesis and the statement q is termed as conclusion.

Solution

Consider the statement into two separate statements

p: Two points lie in a plane

q: Line containing the two points is in the plane

So we can write the given statement “If two points lie in a plane, then the line containing them lies in the plane” as

p q

We are given that two points A and B lie in plane PQR so we can conclude that the line containing the points A and B lie in the plane PQR.

Final Answer:

Hence we can conclude that the line containing points A and B lie in the plane PQR.

### Make a valid conclusion in the situation.

If two points lie in a plane, then the line containing them lies in the plane.

Points A and B lie in plane PQR.

Maths-General

Hint:

Law of Detachment states that if p q is true and it is given that p is true then we can conclude that q is also true. Here, the statement is termed as Hypothesis and the statement q is termed as conclusion.

Solution

Consider the statement into two separate statements

p: Two points lie in a plane

q: Line containing the two points is in the plane

So we can write the given statement “If two points lie in a plane, then the line containing them lies in the plane” as

p q

We are given that two points A and B lie in plane PQR so we can conclude that the line containing the points A and B lie in the plane PQR.

Final Answer:

Hence we can conclude that the line containing points A and B lie in the plane PQR.

Law of Detachment states that if p q is true and it is given that p is true then we can conclude that q is also true. Here, the statement is termed as Hypothesis and the statement q is termed as conclusion.

Solution

Consider the statement into two separate statements

p: Two points lie in a plane

q: Line containing the two points is in the plane

So we can write the given statement “If two points lie in a plane, then the line containing them lies in the plane” as

p q

We are given that two points A and B lie in plane PQR so we can conclude that the line containing the points A and B lie in the plane PQR.

Final Answer:

Hence we can conclude that the line containing points A and B lie in the plane PQR.

Maths-

### The conditional p → q is only false when

a. p = T, q = T

b. p = T, q = F

c. p = F, q = F

d. p = F, q = T

Hint:

p → q is a conditional statement which mean if p then q. The conditional statement is saying that if p is true, then q will immediately follow and thus be true

Solution

The truth table of p → q is given as

Hence, we can see that p → q is only false when p is True and q is False.

Final Answer:

So, p → q is only false when p = T and q = F. Hence option b is correct.

p → q is a conditional statement which mean if p then q. The conditional statement is saying that if p is true, then q will immediately follow and thus be true

Solution

The truth table of p → q is given as

Hence, we can see that p → q is only false when p is True and q is False.

Final Answer:

So, p → q is only false when p = T and q = F. Hence option b is correct.

### The conditional p → q is only false when

a. p = T, q = T

b. p = T, q = F

c. p = F, q = F

d. p = F, q = T

Maths-General

Hint:

p → q is a conditional statement which mean if p then q. The conditional statement is saying that if p is true, then q will immediately follow and thus be true

Solution

The truth table of p → q is given as

Hence, we can see that p → q is only false when p is True and q is False.

Final Answer:

So, p → q is only false when p = T and q = F. Hence option b is correct.

p → q is a conditional statement which mean if p then q. The conditional statement is saying that if p is true, then q will immediately follow and thus be true

Solution

The truth table of p → q is given as

Hence, we can see that p → q is only false when p is True and q is False.

Final Answer:

So, p → q is only false when p = T and q = F. Hence option b is correct.

Maths-

### Use p and q to write the symbolic statement in words.

p: Roses are red.

q: Roses are beautiful.

I) p → q

II) ~q

III) ~q → ~p

Hint:

p → q represents the conditional statement which means “if p then q” or “p implies q”

“ ~ ” symbol represents the inverse of a statement and inverse of a conditional statement like p → q is given as ~p → ~q which means if not p then not q

Solution

It is given

p: Roses are red.

q: Roses are beautiful.

Symbolic statement of p → q is “ If Roses are red, then the roses are beautiful. ”

Symbolic statement of ~q is “ Roses are not beautiful ”

Symbolic statement of ~q → ~p is “ If Roses are not red, then the roses are not beautiful. ”

Final Answer:

p → q : If Roses are red, then the roses are beautiful

~q: Roses are not beautiful

~q → ~p: If Roses are not red, then the roses are not beautiful.

p → q represents the conditional statement which means “if p then q” or “p implies q”

“ ~ ” symbol represents the inverse of a statement and inverse of a conditional statement like p → q is given as ~p → ~q which means if not p then not q

Solution

It is given

p: Roses are red.

q: Roses are beautiful.

Symbolic statement of p → q is “ If Roses are red, then the roses are beautiful. ”

Symbolic statement of ~q is “ Roses are not beautiful ”

Symbolic statement of ~q → ~p is “ If Roses are not red, then the roses are not beautiful. ”

Final Answer:

p → q : If Roses are red, then the roses are beautiful

~q: Roses are not beautiful

~q → ~p: If Roses are not red, then the roses are not beautiful.

### Use p and q to write the symbolic statement in words.

p: Roses are red.

q: Roses are beautiful.

I) p → q

II) ~q

III) ~q → ~p

Maths-General

Hint:

p → q represents the conditional statement which means “if p then q” or “p implies q”

“ ~ ” symbol represents the inverse of a statement and inverse of a conditional statement like p → q is given as ~p → ~q which means if not p then not q

Solution

It is given

p: Roses are red.

q: Roses are beautiful.

Symbolic statement of p → q is “ If Roses are red, then the roses are beautiful. ”

Symbolic statement of ~q is “ Roses are not beautiful ”

Symbolic statement of ~q → ~p is “ If Roses are not red, then the roses are not beautiful. ”

Final Answer:

p → q : If Roses are red, then the roses are beautiful

~q: Roses are not beautiful

~q → ~p: If Roses are not red, then the roses are not beautiful.

p → q represents the conditional statement which means “if p then q” or “p implies q”

“ ~ ” symbol represents the inverse of a statement and inverse of a conditional statement like p → q is given as ~p → ~q which means if not p then not q

Solution

It is given

p: Roses are red.

q: Roses are beautiful.

Symbolic statement of p → q is “ If Roses are red, then the roses are beautiful. ”

Symbolic statement of ~q is “ Roses are not beautiful ”

Symbolic statement of ~q → ~p is “ If Roses are not red, then the roses are not beautiful. ”

Final Answer:

p → q : If Roses are red, then the roses are beautiful

~q: Roses are not beautiful

~q → ~p: If Roses are not red, then the roses are not beautiful.

Maths-

### Make a valid conclusion in the situation.

If cost price > selling price, then the transaction suffers loss.

Cost price = $255 and selling price = $230.

Hint:

Law of Detachment states that if p q is true and it is given that p is true then we can conclude that q is also true. Here, the statement is termed as Hypothesis and the statement q is termed as conclusion.

Solution

Consider the statement into two separate statements

p: Cost price > Selling price

q: The transaction suffers loss

So we can write the given statement “If cost price > selling price, then the transaction suffers loss” as:

p q

We are given

Cost price = $255 and Selling price = $230

Here, Cost price > Selling price so we can say that the p statement is true and hence we can conclude that the q statement is also true i .e the transaction suffers loss.

Final Answer:

Hence we can conclude that the transaction suffers loss.

Law of Detachment states that if p q is true and it is given that p is true then we can conclude that q is also true. Here, the statement is termed as Hypothesis and the statement q is termed as conclusion.

Solution

Consider the statement into two separate statements

p: Cost price > Selling price

q: The transaction suffers loss

So we can write the given statement “If cost price > selling price, then the transaction suffers loss” as:

p q

We are given

Cost price = $255 and Selling price = $230

Here, Cost price > Selling price so we can say that the p statement is true and hence we can conclude that the q statement is also true i .e the transaction suffers loss.

Final Answer:

Hence we can conclude that the transaction suffers loss.

### Make a valid conclusion in the situation.

If cost price > selling price, then the transaction suffers loss.

Cost price = $255 and selling price = $230.

Maths-General

Hint:

Law of Detachment states that if p q is true and it is given that p is true then we can conclude that q is also true. Here, the statement is termed as Hypothesis and the statement q is termed as conclusion.

Solution

Consider the statement into two separate statements

p: Cost price > Selling price

q: The transaction suffers loss

So we can write the given statement “If cost price > selling price, then the transaction suffers loss” as:

p q

We are given

Cost price = $255 and Selling price = $230

Here, Cost price > Selling price so we can say that the p statement is true and hence we can conclude that the q statement is also true i .e the transaction suffers loss.

Final Answer:

Hence we can conclude that the transaction suffers loss.

Law of Detachment states that if p q is true and it is given that p is true then we can conclude that q is also true. Here, the statement is termed as Hypothesis and the statement q is termed as conclusion.

Solution

Consider the statement into two separate statements

p: Cost price > Selling price

q: The transaction suffers loss

So we can write the given statement “If cost price > selling price, then the transaction suffers loss” as:

p q

We are given

Cost price = $255 and Selling price = $230

Here, Cost price > Selling price so we can say that the p statement is true and hence we can conclude that the q statement is also true i .e the transaction suffers loss.

Final Answer:

Hence we can conclude that the transaction suffers loss.

Maths-

### Make a valid conclusion in the situation.

If cost price < selling price, then the transaction makes profit.

Cost price = $100 and selling price = $150.

Hint:

Law of Detachment states that if p q is true and it is given that p is true then we can conclude that q is also true. Here, the statement is termed as Hypothesis and the statement q is termed as conclusion.

Solution

Consider the statement into two separate statements

p: Cost price < Selling price

q: The transaction makes profit

So we can write the given statement “If cost price < selling price, then the transaction makes profit” as:

p q

We are given

Cost price = $100 and Selling price = $150

Here, Cost price < Selling price so we can say that the p statement is true and hence we can conclude that the q statement is also true i .e the transaction makes profit.

Final Answer:

Hence we can conclude that the transaction makes profit.

Law of Detachment states that if p q is true and it is given that p is true then we can conclude that q is also true. Here, the statement is termed as Hypothesis and the statement q is termed as conclusion.

Solution

Consider the statement into two separate statements

p: Cost price < Selling price

q: The transaction makes profit

So we can write the given statement “If cost price < selling price, then the transaction makes profit” as:

p q

We are given

Cost price = $100 and Selling price = $150

Here, Cost price < Selling price so we can say that the p statement is true and hence we can conclude that the q statement is also true i .e the transaction makes profit.

Final Answer:

Hence we can conclude that the transaction makes profit.

### Make a valid conclusion in the situation.

If cost price < selling price, then the transaction makes profit.

Cost price = $100 and selling price = $150.

Maths-General

Hint:

Law of Detachment states that if p q is true and it is given that p is true then we can conclude that q is also true. Here, the statement is termed as Hypothesis and the statement q is termed as conclusion.

Solution

Consider the statement into two separate statements

p: Cost price < Selling price

q: The transaction makes profit

So we can write the given statement “If cost price < selling price, then the transaction makes profit” as:

p q

We are given

Cost price = $100 and Selling price = $150

Here, Cost price < Selling price so we can say that the p statement is true and hence we can conclude that the q statement is also true i .e the transaction makes profit.

Final Answer:

Hence we can conclude that the transaction makes profit.

Law of Detachment states that if p q is true and it is given that p is true then we can conclude that q is also true. Here, the statement is termed as Hypothesis and the statement q is termed as conclusion.

Solution

Consider the statement into two separate statements

p: Cost price < Selling price

q: The transaction makes profit

So we can write the given statement “If cost price < selling price, then the transaction makes profit” as:

p q

We are given

Cost price = $100 and Selling price = $150

Here, Cost price < Selling price so we can say that the p statement is true and hence we can conclude that the q statement is also true i .e the transaction makes profit.

Final Answer:

Hence we can conclude that the transaction makes profit.

Maths-

### Make a valid conclusion in the situation.

If you have more than $1000, then you can buy a music system.

You have $1200.

Hint:

Law of Detachment states that if p q is true and it is given that p is true then we can conclude that q is also true. Here, the statement is termed as Hypothesis and the statement q is termed as conclusion.

Solution

Consider the statement into two separate statements

p: You have more than $1000

q: You can buy a music system

So we can write the given statement “If you have more than $1000, then you can buy a music system” as:

p q

We are given that we have $1200 and $1200 > $1000 so we can say that the p statement is true and hence we can conclude that the q statement is also true i.e we can buy a music system.

Final Answer:

Hence we can conclude that we can buy a music system.

Law of Detachment states that if p q is true and it is given that p is true then we can conclude that q is also true. Here, the statement is termed as Hypothesis and the statement q is termed as conclusion.

Solution

Consider the statement into two separate statements

p: You have more than $1000

q: You can buy a music system

So we can write the given statement “If you have more than $1000, then you can buy a music system” as:

p q

We are given that we have $1200 and $1200 > $1000 so we can say that the p statement is true and hence we can conclude that the q statement is also true i.e we can buy a music system.

Final Answer:

Hence we can conclude that we can buy a music system.

### Make a valid conclusion in the situation.

If you have more than $1000, then you can buy a music system.

You have $1200.

Maths-General

Hint:

Law of Detachment states that if p q is true and it is given that p is true then we can conclude that q is also true. Here, the statement is termed as Hypothesis and the statement q is termed as conclusion.

Solution

Consider the statement into two separate statements

p: You have more than $1000

q: You can buy a music system

So we can write the given statement “If you have more than $1000, then you can buy a music system” as:

p q

We are given that we have $1200 and $1200 > $1000 so we can say that the p statement is true and hence we can conclude that the q statement is also true i.e we can buy a music system.

Final Answer:

Hence we can conclude that we can buy a music system.

Law of Detachment states that if p q is true and it is given that p is true then we can conclude that q is also true. Here, the statement is termed as Hypothesis and the statement q is termed as conclusion.

Solution

Consider the statement into two separate statements

p: You have more than $1000

q: You can buy a music system

So we can write the given statement “If you have more than $1000, then you can buy a music system” as:

p q

We are given that we have $1200 and $1200 > $1000 so we can say that the p statement is true and hence we can conclude that the q statement is also true i.e we can buy a music system.

Final Answer:

Hence we can conclude that we can buy a music system.

Maths-

### Make a valid conclusion in the situation.

If 𝑛 < 5, then (−𝑛) > (−5).

The value of 𝑛 is 3.

Hint:

Law of Detachment states that if p q is true and it is given that p is true then we can conclude that q is also true. Here, the statement is termed as Hypothesis and the statement q is termed as conclusion.

Solution

Consider the statement into two separate statements

p: 𝑛 < 5

q: (−𝑛) > (−5)

So we can write the given statement “If 𝑛 < 5, then (−𝑛) > (−5)” as:

p q

We are given

n = 3

Here, 3 < 5 so we can say that the p statement is true and hence we can conclude that the q statement is also true i.e (−3) > (−5).

Final Answer:

Hence we can conclude that (−3) > (−5).

Law of Detachment states that if p q is true and it is given that p is true then we can conclude that q is also true. Here, the statement is termed as Hypothesis and the statement q is termed as conclusion.

Solution

Consider the statement into two separate statements

p: 𝑛 < 5

q: (−𝑛) > (−5)

So we can write the given statement “If 𝑛 < 5, then (−𝑛) > (−5)” as:

p q

We are given

n = 3

Here, 3 < 5 so we can say that the p statement is true and hence we can conclude that the q statement is also true i.e (−3) > (−5).

Final Answer:

Hence we can conclude that (−3) > (−5).

### Make a valid conclusion in the situation.

If 𝑛 < 5, then (−𝑛) > (−5).

The value of 𝑛 is 3.

Maths-General

Hint:

Law of Detachment states that if p q is true and it is given that p is true then we can conclude that q is also true. Here, the statement is termed as Hypothesis and the statement q is termed as conclusion.

Solution

Consider the statement into two separate statements

p: 𝑛 < 5

q: (−𝑛) > (−5)

So we can write the given statement “If 𝑛 < 5, then (−𝑛) > (−5)” as:

p q

We are given

n = 3

Here, 3 < 5 so we can say that the p statement is true and hence we can conclude that the q statement is also true i.e (−3) > (−5).

Final Answer:

Hence we can conclude that (−3) > (−5).

Law of Detachment states that if p q is true and it is given that p is true then we can conclude that q is also true. Here, the statement is termed as Hypothesis and the statement q is termed as conclusion.

Solution

Consider the statement into two separate statements

p: 𝑛 < 5

q: (−𝑛) > (−5)

So we can write the given statement “If 𝑛 < 5, then (−𝑛) > (−5)” as:

p q

We are given

n = 3

Here, 3 < 5 so we can say that the p statement is true and hence we can conclude that the q statement is also true i.e (−3) > (−5).

Final Answer:

Hence we can conclude that (−3) > (−5).