Question

1. conditional statement/converse

a. the converse does what to the
conditional statement?

b. write the converse of the following
statement: \if a figure is a triangle,
then the angles add to 180.

notes:

Explanation:

Part A

A conditional statement has the form "If \( p \), then \( q \)" (where \( p \) is the hypothesis and \( q \) is the conclusion). The converse of a conditional statement interchanges the hypothesis and the conclusion. So, the converse takes the conclusion of the original conditional statement and makes it the hypothesis, and takes the hypothesis of the original conditional statement and makes it the conclusion. In other words, the converse of "If \( p \), then \( q \)" is "If \( q \), then \( p \)".

Step 1: Identify the hypothesis and conclusion

In the given statement "If a figure is a triangle, then the angles add to 180", the hypothesis (\( p \)) is "a figure is a triangle" and the conclusion (\( q \)) is "the angles add to 180".

Step 2: Form the converse

To form the converse, we interchange the hypothesis and the conclusion. So we take \( q \) as the new hypothesis and \( p \) as the new conclusion.

Answer:

The converse interchanges the hypothesis and the conclusion of the conditional statement (i.e., if the conditional is "If \( p \), then \( q \)", the converse is "If \( q \), then \( p \)").

Part B