Solution

The correct answer is \(\overline{P \oplus Q}\)

Key Points

• XOR operator ⊕ is both commutative and associative.
  • A ⊕ B = AB̅ + A̅.B
  • A ⊕ A = 0
  • 1 ⊕ A = A̅
  • 0 ⊕ A = A

COLCULATION:

1. F(P, Q) = ((1 ⊕ P) ⊕(P⊕Q)) ⊕((P⊕Q) ⊕(Q⊕0) )
2. F(P, Q) = 1 ⊕ (P ⊕ P) ⊕ Q ⊕ P⊕ (Q  ⊕ Q) ⊕ 0
3. F(P, Q) = (1 ⊕ 0) ⊕ Q ⊕ P⊕ (0 ⊕ 0)
4. F(P, Q) = (1 ⊕ Q) ⊕ (P⊕ 0)
5. F(P, Q) = Q̅  ⊕  P
6. F(P, Q) = Q̅. P̅ + Q.P
7. F(P, Q) = P ⊙ Q 
8. F(P, Q) = \(\overline {P \oplus Q} \)