Logical Identities

Example 1: State the converse and contrapositive of the following statements:

(a) If it rains, I am not going.

(b) I will stay only if you go.

(c) If you get 8 pounds, you can bake the cake.

(d) I can’t complete the task if I don’t get more help.

Solution

(a) Converse: If I don’t go, then it rains.

Contrapositive: If I go, then it does not rain.

(b) Converse: If you go then I will stay

Contrapositive: If you go I will not stay

(c) Converse: If you can bake the cake you get 8 pounds.

Contrapositive:If you cannot bake the cake you don’t get 8 pounds.

(d)Converse: I don’t get more help if I can’t complete the task.

Contrapositive: I can complete the the task if I get more help.

Example 2: For each of the following expressions, use identities to find equivalent expressions which use onlyÙ andØ and are as simple as possible.

Solution: