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 option is correct

Answer 2

A. A polygon is not a pentagon if and only if it does not have five sides 
is the answer as,
The given statement is of the form: 
A implies B.
or A ⇒ B
Negating both sides gives us
not(A) implies not(B)
or ¬A ⇒ ¬B.
Therefore, if both A and B are negative, the relation will hold true.
I'm sorry if that was too much of mathematical jargon.
Though, I hope you understand...