State and prove De-Morgan’s laws in boolean algebra. DeMorgan’s theorem states that:

Question

State and prove De-Morgan’s laws in boolean algebra.

Answer 1

De-Morgan’s theorem states that:

(i) (X+Y)’=X’.Y’

(ii) (X.Y)’=X’+Y’

Now ,let us prove using truth table:

(i) (X+Y)’=X’.Y’

Hence, (X + Y)' = X'.Y'

(ii) (X.Y)’=X’+Y’

Hence, (X.Y)' = X' + Y'