Chapter 2.4, Problem 16PPS

To determine

To find: Whether the stated conclusion is valid based on the given information, if not, write invalid.

Answer to Problem 16PPS

The conclusion is valid.

Explanation of Solution

Given:

Right angles are congruent, and $\angle 1$ , and $\angle 2$ are right angles.

Calculation:

First identify the hypothesis $p$ and the conclusion $q$ of the true conditional.

Let $p$ represents two angles are right angles.

Let $q$ represents two angles are congruent.

Now analyze the conclusion.

The given statement “ $\angle 1$ , and $\angle 2$ are right angles” satisfies the hypothesis, so $p$ is true.

Use the Law of Detachment,

“if $p\to q$ is a true statement and $p$ is true, then $q$ is true.”

Therefore, by the Law of Detachment, the conclusion “ $\angle 1\cong \angle 2$ ”, which matches $q$ , is valid.