Prove the Boolean expression using Boolean laws. Also, mention the law

1.	Prove the Boolean expression using Boolean laws. Also, mention the law used at each step. F = (x’ + z) + [(y’ + z).(x’ + y)]’ = 1
Answer» F =(x’ + z) + [(y’ + z).(x’ + y)]’ = x’ + z + (y’ + z)’ + (x’ + y)’ = x’ + z + (y’)’ z’ + (x’)’ y’ [De Morgan’s Law] = x’ + z + yz’ + xy’ [Double Negation] = x’ + xy’ + z + yz’ [a + a’b = a + b] = x’ + y’ + z + y = x’ + z + y’ + y [Complement Law: a + a’ = 1] = x’ + z + 1 = 1

Prove the Boolean expression using Boolean laws. Also, mention the law used at each step. F = (x’ + z) + [(y’ + z).(x’ + y)]’ = 1

Answer»

F =(x’ + z) + [(y’ + z).(x’ + y)]’

= x’ + z + (y’ + z)’ + (x’ + y)’

= x’ + z + (y’)’ z’ + (x’)’ y’ [De Morgan’s Law]

= x’ + z + yz’ + xy’ [Double Negation]

= x’ + xy’ + z + yz’ [a + a’b = a + b]

= x’ + y’ + z + y = x’ + z + y’ + y [Complement Law: a + a’ = 1]

= x’ + z + 1

= 1