Question

Kellie is given the following information:

If two lines are perpendicular, then they intersect at a right angle. Lines A and B are perpendicular.

She concludes that lines A and B intersect at a right angle. Which statements are true? Check all that apply.

She used inductive reasoning.
She used the law of detachment.
Her conclusion is valid.
The statements can be represented as "if p, then q and if q, then r."
Her conclusion is true.

Answer 1

it's b, c, e

Explanation:

Answer 2

She used inductive reasoning. (False)

She used the law of detachment. (True)

Her conclusion is valid. (True)

The statements can be represented as "if p, then q and if q, then r." (False)

Her conclusion is true. (True)

Explanation:

p = Two lines are perpendicular

q = They intersect at Right angles.

Given: A and B are perpendicular

Conclusion: A and B intersect at right angle.

According to the law of detachment, There are two premises (statements that are accepted as true) and a conclusion. They must follow the pattern as shown below.

Statement 1: If p, then q.

Statement 2: p

Conclusion: q

In our case the pattern is followed. The truth of the premises logically guarantees the truth of the conclusion. So her conclusion is true and valid.