Question

1. write the conditional statement p -> q, the converse q -> p, the inverse -p -> -q, and the contrapositive -q -> -p. then decide if the statement is true or false. see example 3 let p be “two angles are supplementary” and let q be “the measures of the angles sum to 180°.”

Explanation:

Step1: Write the conditional statement

The conditional statement $p
ightarrow q$ is: If two angles are supplementary, then the measures of the angles sum to $180^{\circ}$. This is true by the definition of supplementary angles.

Step2: Write the converse statement

The converse statement $q
ightarrow p$ is: If the measures of the angles sum to $180^{\circ}$, then two angles are supplementary. This is also true by the definition of supplementary angles.

Step3: Write the inverse statement

The inverse statement $
eg p
ightarrow
eg q$ is: If two angles are not supplementary, then the measures of the angles do not sum to $180^{\circ}$. This is true. If angles are not supplementary, they cannot add up to $180^{\circ}$.

Step4: Write the contra - positive statement

The contra - positive statement $
eg q
ightarrow
eg p$ is: If the measures of the angles do not sum to $180^{\circ}$, then two angles are not supplementary. This is true as well.

Answer:

Conditional ($p
ightarrow q$): True.
Converse ($q
ightarrow p$): True.
Inverse ($
eg p
ightarrow
eg q$): True.
Contra - positive ($
eg q
ightarrow
eg p$): True.