Consider the following Boolean expression of a function F : F(π,π)=β¦
2026
Consider the following Boolean expression of a function F :
F(π,π)= (π'+π)β(π'π)
Which of the following expressions is/are equivalent to F ?
- A.
(Pβπ)'
- B.
Pβπ
- C.
P'βπ
- D.
P'βπ'
Attempted by 42 students.
Show answer & explanation
Correct answer: A, C
Given F(P, Q) = (P' + Q) β (P'Q). Using the definition A β B = AB' + A'B, we substitute A = (P' + Q) and B = P'Q.
The expression becomes (P' + Q)(P'Q)' + (P' + Q)'(P'Q). Applying De Morgan's laws: (P'Q)' = P + Q' and (P' + Q)' = PQ'. Substituting these back, we get F = (P' + Q)(P + Q') + PQ'(P'Q).
The second term simplifies to 0 because P'P = 0. Expanding the first term: P'P + P'Q' + QP + QQ'. Since P'P = 0 and QQ' = 0, this simplifies to P'Q' + PQ.
This expression represents the XNOR operation (P β Q). Thus, F is equivalent to (P β Q)' and also P' β Q.