Question

ASAP PLEASE!!! Start with the following conditional statement: If it is October 31, then it is Halloween.

a. State the converse of the statement.
b. State the inverse of the statement.
c. State the contrapositive of the statement.

Answer 1

Let p, and q be 2 statements. Consider the conditional p⇒q (that is, if p then q).

i) The converse of the statement is q⇒p.

ii). The inverse of the statement is ¬p⇒¬q.

iii). The contrapositive of the statement is ¬q⇒¬p.


Let p: it is October 31, and let q: it is Halloween.

The converse of the conditional p⇒q is q⇒p:

If it is Halloween, then it is October 31.

The inverse is ¬p⇒¬q:

If it is not October 31, then it is not Halloween.

The contrapositive ¬q⇒¬p is:

If it is not Halloween, then it is not October 31.