Question

write the conditional statement p → q, the converse q → p, the inverse ~p → ~q, and the contrapositive ~q → ~p in words. then decide whether each statement is true or false. (see example 3.) 11. 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°. 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°, 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°. This is true because if angles are not supplementary, they don't meet the 180 - degree - sum criteria.

Step4: Write the contrapositive statement

The contrapositive statement $
eg q
ightarrow
eg p$ is: If the measures of the angles do not sum to 180°, then two angles are not supplementary. This is true as it is logically equivalent to the conditional statement.

Answer:

Conditional ($p
ightarrow q$): If two angles are supplementary, then the measures of the angles sum to 180°. (True)
Converse ($q
ightarrow p$): If the measures of the angles sum to 180°, then two angles are supplementary. (True)
Inverse ($
eg p
ightarrow
eg q$): If two angles are not supplementary, then the measures of the angles do not sum to 180°. (True)
Contrapositive ($
eg q
ightarrow
eg p$): If the measures of the angles do not sum to 180°, then two angles are not supplementary. (True)