Simplification of Boolean Expression

Simplification of Boolean Expression:

1. XY’Z’ + XY’Z’W + XZ’
= XY’Z’(1+W) + XZ’
= XY’Z’.1 + XZ’ (Since, 1 + A = 1 i.e. 1 + W = 1)
= XY’Z’ + XZ’
= XZ’ + (Y’ + 1)
= XZ’.1 (Since, 1 + A’ = 1 i.e. 1 + Y’ = 1)
= XZ'

2. AB’ + A’B’ +A’B + AB
= B’(A + A’) + B(A’ + A) = B’.1 + B.1 (Since, A + A’ = 1)
= B’ + B
= 1

3. ABC + AB’C + ABC’ + AB’C’
= AC(B + B’) + AC’( B + B’)
= AC.1 + AC’.1 (Since, B + B’ = 1)
= AC + AC’
= A(C + C’)
= A.1
=A