Question

According to the Principle of Duality, the Boolean equation Q'•0+P'•Q'+P'• Q = P' will be equivalent to:

Options

• Q•0 + P•Q + P•Q' = P

• Q'•1 + P•Q' + P•Q' = P'

• (Q' + 1)•(P' + Q')•(P' + Q) = P'

• (Q' + 0)•(P' + Q')•(P' + Q) = P'

Answer 1

(Q' + 1)•(P' + Q')•(P' + Q) = P'

Explanation:

According to the Principle of Duality, the dual of a Boolean expression is obtained by:

1. Changing each AND (•) operator to an OR (+) operator and vice versa.
2. Replace each identity element 0 with 1 and vice versa.
3. Keeping the variables (P', Q', Q, etc) unchanged.

Applying these rules to the original equation transforms the sums into products and the zeros into ones, matching option (c).