Different Implications

If p and q are two statements then a general implication statement can be given as if p then q, i.e. p→q.

The different forms of implications are as follows:

1. Contrapositive:

If p→q is an implication then its contrapositive is given as ~q→~p.

For example, find contrapositive of following statement:

If n is a multiple of 6, then n is a multiple of 12.

Contrapositive: If n is not a multiple of 12, then n is not a multiple of 6.

A  statement and its contrapositive are logically equivalent.

2. Converse:

If p→q is an implication then its converse is given as q→p.

For example, find converse of the following statement:

If a and b are odd numbers then a+b is an even number.

Converse: If a+b is an even number then a and b are odd numbers.

A statement and its converse are not logically equivalent.

3. Inverse:

If p→q is an implication then its inverse is given as ~p→~q.

For example, find inverse of the following statement:

If a student gets 60% then student gets first class.

Inverse: If a student doesn’t get 60% then student doesn’t get first class.

A statement and its inverse are logically equivalent.