Chapter 1.8, Problem 7PSB

To determine

To write down the sentence in conditional form and to determine the converse, the inverse, and the contrapositive of statement.

Answer to Problem 7PSB

Conditional form of given sentence is “If it is square, then a quadrilateral has four congruent sides.”

Explanation of Solution

Given information:

The given sentence is “A square is a quadrilateral with four congruent sides.”

Every conditional statement “If p, then q” has three other statements associated with it.

A converse (If q, then p)

An inverse $(If~p,then~q.)$

A contrapositive $(If~q,then~p.)$

By referring to above associated statements, we can write:

Converse: “If a quadrilateral has four congruent sides, then it is a square.”

Inverse: “If a polygon is not a square, then it is not a quadrilateral with four congruent sides.”

Contrapositive: “If a quadrilateral does not have four congruent sides, then it is not a square.”