The Logic expression (P′ ∧ Q) ∪ (P ∧ Q′) ∪ (P ∧ Q) is equivalent to:
2022
The Logic expression (P′ ∧ Q) ∪ (P ∧ Q′) ∪ (P ∧ Q) is equivalent to:
- A.
P′ ∪ Q
- B.
P ∪ Q′
- C.
P ∪ Q
- D.
P′ ∪ Q′
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Correct answer: C
(P′ ∧ Q) ∪ (P ∧ Q′) ∪ (P ∧ Q)
Step 1: Combine last two terms
(P ∧ Q′) ∪ (P ∧ Q)
Take P common: =P∧(Q′∪Q)
Q′∪Q=1
P∧1 = P
So expression becomes: (P′Q)∪P
Step 2: Apply absorption law P∪(P′Q)
Use identity: A∪(A′B)=A∪B
=P∪Q
C) P∪Q
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