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If the Boolean expression (p ⊕ q) ∧ (~p ⊙ q) is equivalent to p ∧ q, where ⊕, ⊙ ∈ {∧, ∨} then the ordered pair (⊕, ⊙) is:

1. (∨, ∧)
2. (∨, ∨)
3. (∧, ∨)
4. (∧, ∧)

Correct answer: (∧, ∨)

Solution

Testing all four values, (p AND q) AND (~p OR q) reduces to p AND q for all p,q. So the ordered pair is (AND, OR), i.e. option (∧, ∨).

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