Which statement is logically equivalent to the following conditional statement?

If it has five sides, then it is not an octagon.

If it is not an octagon, then it has five sides.

If it does not have five sides, then it is not an octagon.

If it does not have five sides, then it is an octagon.

If it is an octagon, then it does not have five sides.

Question

Which statement is logically equivalent to the following conditional statement?

If it has five sides, then it is not an octagon.

If it is not an octagon, then it has five sides.

 If it does not have five sides, then it is not an octagon.

 If it does not have five sides, then it is an octagon.

 If it is an octagon, then it does not have five sides.

anonymous · Answer

The conditional and the contrapositive are logically equivalent.

The conditional is of the form:  if p, then q.
The contrapositive is of the form:  if not q, then not p.

Do you see which statement is the contrapositive of "If it has five sides, then it is not an octagon" ?