Question

question 1-12
a pentagon has exactly 5 sides. prove the following conditional by proving the contrapositive. if a polygon does not have exactly 5 sides, then it is not a pentagon
contrapositive: if a polygon is a pentagon, then the polygon has 5 sides. since a pentagon has 5 sides, the contrapositive is true
since the contrapositive is true, the original sta

Explanation:

Step1: Recall contrapositive concept

The contrapositive of "if p then q" is "if not q then not p". Here p is "a polygon does not have exactly 5 sides" and q is "it is not a pentagon". Its contrapositive is "if a polygon is a pentagon, then the polygon has 5 sides".

Step2: Evaluate contrapositive truth

By definition, a pentagon has 5 sides, so the contrapositive is true. Since a conditional and its contrapositive have the same truth - value, the original conditional is true.

Answer:

The original conditional "If a polygon does not have exactly 5 sides, then it is not a pentagon" is true because its contrapositive "If a polygon is a pentagon, then the polygon has 5 sides" is true.