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Question
If the Boolean expression (p⊕q)∧(∼p⊙q) is equivalent to p∧q, where ⊕,⊙ϵ{∧,∨}, then the order pair (⊕,⊙) is
If the Boolean expression (p⊕q)∧(∼p⊙q) is equivalent to p∧q, where ⊕,⊙ϵ{∧,∨}, then the order pair (⊕,⊙) is
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Solution
The correct option is A (∧,∨)
(p⊕q)∧(∼p⊙q)≡p∧q (given)
p q ∼p p∧q p∨q ∼p∨q ∼p∧q (p∧q)∧(∼p∨q) T T F T T T F T T F F F T F F F F T T F T T T F F F T F F T F F
from truth table (⊕,⊙)=(∧,∨).
(p⊕q)∧(∼p⊙q)≡p∧q (given)
| p | q | ∼p | p∧q | p∨q | ∼p∨q | ∼p∧q | (p∧q)∧(∼p∨q) |
| T | T | F | T | T | T | F | T |
| T | F | F | F | T | F | F | F |
| F | T | T | F | T | T | T | F |
| F | F | T | F | F | T | F | F |
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