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Which of the following compound statements is logically equivalent to (p AND q)?

1. p -> ~q
2. ~p OR ~q
3. ~(p -> ~q)
4. ~(~p AND ~q)

Correct answer: ~(p -> ~q)

Solution

Since p -> ~q is equivalent to ~p OR ~q, its negation ~(p -> ~q) becomes p AND q by De Morgan's law.

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