28 Prove the following tautologies by starting with the left

28. Prove the following tautologies by starting with the left side and finding a series of equivalent wffs that will convert the left side into the right side. You may use any of the equivalencies in the list on page 9 or the equivalencies from Exercise 26.

Solution

Prove for given statements using truth table :

For a.:

Since values of column 6 and 8 are equal the given statement a. is true.

For c.:

Since values of column 5 and 6 are equal the given statement c. is also true.

A	B	B\'	A^B\'	(A^B\')\'	(A^B\')\'vB	A\'	A\'VB
0	0	1	0	1	1	1	1
0	1	0	0	1	1	1	1
1	0	1	1	0	0	0	0
1	1	0	0	1	1	0	1