Question

"A polygon is a pentagon if and only if it has five sides."If this statement is true, then which of the following statements must also be true?

A.A polygon is not a pentagon if and only if it does not have five sides.
B.A polygon is not a pentagon if and only if it has five sides.
C.A polygon is a pentagon if and only if it does not have five sides.
D.A polygon does not have five sides if and only if it is a pentagon.

Answer 1

A.A polygon is not a pentagon if and only if it does not have five sides.

Step-by-step explanation:

This can be confusing, but a pentagon is a five-sided polygon, so all polygons with 5 sides are pentagons, from the name penta-five is indicated, so any polygon which has any number different of sides to five is not a polygon, that´s why the correct option is A.A polygon is not a pentagon if and only if it does not have five sides., since its a double negation its confusing, but remember this, double negative is a positive, so A polygon is a pentagon if it has five sides.