Mathematics

Grade9

Easy

Question

# Determine if statement (3) follows from statements (1) and (2) by what law.

1) If an angle measures more than 90 degrees, then it is not acute.

2) m angle ABC = 120 degrees.

3) Angle ABC is not acute.

- Law of Detachment
- Law of Syllogism
- Invalid

Hint:

### In deductive reasoning we use facts, definitions and postulates to draw a conclusion. There are two laws under deductive reasoning they are Law of Detachment and Law of Syllogism. Here, we have to determine which of these laws in applied here to draw the conclusion.

## The correct answer is: Law of Detachment

### In the question it is given that,

1) If an angle measures more than 90 degrees, then it is not acute.

2) m angle ABC = 120 degrees.

3) Angle ABC is not acute.

Here, we have to determine the law which the above statements obey.

Let statement (1) be p, statement (2) be q and statement (3) be r.

From the given statement we can say that p equals to q and r the conclusion drawn from p and q.

So, the statement (3) is true for statement (1) and (2).

Thus, the above statements obey the Law of Detachment.

Therefore, the correct option is Law of Detachment.

In Law of Syllogism if a statement p equals q and if q equals r, then p equals r whereas in Law of Detachment if a statement p equals q where p is true then q is also true.