Boolean Algebra and Logic Simplification - Technical MCQs

Q1:

When are the inputs to a NAND gate, according to De Morgan's theorem, the output expression could be:

A X = A + B

B

C X = (A)(B)

D

ANS:A - X = A + B

A AND B = A*B
A NAND B = BAR(A*B)
BAR(A) NAND BAR(B) = BAR[BAR(A)* BAR(B)]
According to DeMorgan's Theorem:
BAR[BAR(A)* BAR(B)] = BAR[BAR(A)] + BAR[BAR(B)]
According to Double negation Theorem:
BAR[BAR(A)] + BAR[BAR(B)] = BAR(A) + BAR(B)