Maths-
General
Easy
Question
Make and test a conjecture about the sign of the cube of negative integers.
Hint:
Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.
Deductive reasoning is the process by which a person makes conclusions based on previously known facts.
The correct answer is: Hence, we conclude that the cube of negative integers is also an negative integer and we have proved this conjecture by deductive reasoning
Let’s create a conjecture for the negative integers -2, -7 and -9. We are asked to make a conjecture about the sign of cube of negative integers.
So first, do the cube of the assumed negative integers. We got
(-2)3 = -8
(-7)3 = -343
(-9)3 = -729
So, we conclude that the cube of negative integers will also be an negative integer and this is the conjecture.
Now, let’s see if the conjecture is true or not by deductive reasoning. Let’s say the negative is -x.
Taking the cube of -x
(-x)2 = -x × (-x) × (-x)
= -x3
We can see that the cube of negative integers is also an negative integer.
Final Answer:
Hence, we conclude that the cube of negative integers is also an negative integer and we have proved this conjecture by deductive reasoning
Related Questions to study
Maths-
In the following system of linear equations, k is a constant and x and y are variables. For what value of k will the system of equations have infinitely many solution?
kx - 3y = 12
4x - 5y = 20
In the following system of linear equations, k is a constant and x and y are variables. For what value of k will the system of equations have infinitely many solution?
kx - 3y = 12
4x - 5y = 20
Maths-General
Maths-
In the following system of linear equations, k is a constant and x and y are variables. For what value of k will the system of equations have no solution?
kx - 3y = 4
4x - 5y = 7
In the following system of linear equations, k is a constant and x and y are variables. For what value of k will the system of equations have no solution?
kx - 3y = 4
4x - 5y = 7
Maths-General
Maths-
Determine whether the following equations have unique solution y = 2x + 5
y = 3x – 2.
Determine whether the following equations have unique solution y = 2x + 5
y = 3x – 2.
Maths-General
Maths-
Solve the following equation : 2(1 - x) + 5x = 3(x + 1) and say whether it is having one solution , no solution or infinitely many solutions ?
Solve the following equation : 2(1 - x) + 5x = 3(x + 1) and say whether it is having one solution , no solution or infinitely many solutions ?
Maths-General
Maths-
Given five noncollinear points, make a conjecture about the number of ways to connect different pairs of points.
Given five noncollinear points, make a conjecture about the number of ways to connect different pairs of points.
Maths-General
Maths-
Check, whether the following equation has exactly one solution or infinitely many solution or no solution. 4x + 2 = 4x – 5
Check, whether the following equation has exactly one solution or infinitely many solution or no solution. 4x + 2 = 4x – 5
Maths-General
Maths-
Write the converse and biconditional statement for the given conditional statement.
If a triangle is equilateral, then it is equiangular.
Write the converse and biconditional statement for the given conditional statement.
If a triangle is equilateral, then it is equiangular.
Maths-General
Maths-
Check, whether the following equation has exactly one solution or infinitely many solution or no solution. 4x - 5 = 2(2x - 1) – 3
Check, whether the following equation has exactly one solution or infinitely many solution or no solution. 4x - 5 = 2(2x - 1) – 3
Maths-General
Maths-
The system of equations 3x - 5y = 20 ; 6x - 10y = 40 has
The system of equations 3x - 5y = 20 ; 6x - 10y = 40 has
Maths-General
Maths-
Describe the pattern in the numbers. Write the next number in the pattern.
7, 3.5, 1.75, 0.875, …
Describe the pattern in the numbers. Write the next number in the pattern.
7, 3.5, 1.75, 0.875, …
Maths-General
Maths-
Check, whether the following equation has exactly one solution or infinitely many solution or no solution. 4x - 3 = 2x + 13
Check, whether the following equation has exactly one solution or infinitely many solution or no solution. 4x - 3 = 2x + 13
Maths-General
Maths-
Describe the pattern in the numbers. Write the next number in the pattern.
5, − 2, − 9, − 16, …
Describe the pattern in the numbers. Write the next number in the pattern.
5, − 2, − 9, − 16, …
Maths-General
Maths-
Use the Law of Detachment to make a valid conclusion in the true situation. Alex goes to the park every Sunday evening. Today is Sunday.
Use the Law of Detachment to make a valid conclusion in the true situation. Alex goes to the park every Sunday evening. Today is Sunday.
Maths-General
Maths-
For which of the values of a and b will the following pair of linear equations has infinitely many solutions x + 2y = 1; (a - b)x + (a + b)y = a + b - 2
a) a = - 3 , b = 1
b) a = 3 , b = 1
c) a = 2 , b = 2
d) None of the above
For which of the values of a and b will the following pair of linear equations has infinitely many solutions x + 2y = 1; (a - b)x + (a + b)y = a + b - 2
a) a = - 3 , b = 1
b) a = 3 , b = 1
c) a = 2 , b = 2
d) None of the above
Maths-General
Maths-
Describe the pattern in the numbers. Write the next number in the pattern.
3, 1, 1/3, 1/9, …
Describe the pattern in the numbers. Write the next number in the pattern.
3, 1, 1/3, 1/9, …
Maths-General