Question

Let p represent: A polygon has three sides.

Let q represent: A polygon is a triangle.
What is the verbal expression of the following statement?
Statement: A polygon does not have three sides if and only if it is not a triangle.

A. A polygon does not have three sides if and only if it is a triangle.
B. A polygon has three sides if and only if it is a triangle.
C. If a polygon does not have three sides, then it is a triangle.
D. A polygon does not have three sides if and only if it is not a triangle.

Answer 1

The verbal expression of the statement is: A polygon does not have three sides if and only if it is not a triangle.

Step-by-step explanation:

The verbal expression of the statement is: A polygon does not have three sides if and only if it is not a triangle.

This can be represented using logical symbols as: !p ⇔ !q.

Translated into words, this means: If a polygon does not have three sides, then it is not a triangle, and conversely, if a polygon is not a triangle, then it does not have three sides.