Page 174 - FUNDAMENTALS OF COMPUTER

NPP

174 Fundamentals of Computers NPP

Problem 3.24 àíZ 3.24
Prove that: {gÕ H$s{OE {H$:

A + AB = A + . B
Solution: hc:

Taking Left Hand Side as Y, Y

Y = A + A B .
Complement both the sides

Y = A + AB.
Applying De Morgan’s Laws

Y = A AB. .

Y = A  .   A + B  

Y = A . ( A + B )

Y = A A +. A B.

Y = 0 + A B .

Y = AB.
Complement both the sides

Y = AB.

Y = A + B
Y = A + B
Y = Right Hand Side, Hence we prove that
A + AB = A + . B

Shortcut Method
Since, A + B.C = (A + B).(A + C)

Thus, A + A .B = (A A).(A B)
+
+
But + AA 1
=
Therefore, A + = A.B (A B) Hence Proved.
+