what is the inverse of the conditional statement? if a polygon has five angles, then it is a pentagon. if a polygon is a pentagon, then it has five angles. if a polygon is not a pentagon, then it does not have five angles. if a polygon does not have five angles, then it is not a pentagon. if a polygon has five angles, then it is not a pentagon.

Question

Accepted Answer

# Brief Explanations:
A conditional statement is in the form "If $p$, then $q$". The inverse of a conditional statement "If $p$, then $q$" is "If not $p$, then not $q$".
In the given statement "If a polygon has five angles ($p$), then it is a pentagon ($q$)", we need to find the inverse.
The first option "If a polygon is a pentagon ($q$), then it has five angles ($p$)" is the converse (swapping $p$ and $q$).
The second option "If a polygon is not a pentagon (not $q$), then it does not have five angles (not $p$)" is the contrapositive (swapping and negating $p$ and $q$).
The third option "If a polygon does not have five angles (not $p$), then it is not a pentagon (not $q$)" is the inverse (negating $p$ and $q$).
The fourth option "If a polygon has five angles ($p$), then it is not a pentagon (not $q$)" is neither the inverse, converse, nor contrapositive.

# Answer:
If a polygon does not have five angles, then it is not a pentagon.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Answer: