Multiple choice

$P$ and $Q$ are two propositions. Which of the following logical expressions are equivalent?

I. $P ∨ \neg Q$ ||. $\neg(\neg P ∧ Q)$ |||. $(P ∧ Q) ∨ (P ∧ \neg Q) ∨ (\neg P ∧ \neg Q)$ IV. $(P ∧ Q) ∨ (P ∧ \neg Q) ∨ (\neg P ∧ Q)$

  1. Only I and II

  2. Only I, II and III

  3. Only I, II and IV

  4. All of I, II III and IV
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$(P ∧ Q) ∨ (P ∧ \neg Q) ∨ (\neg P ∧ \neg Q)$ = $ P ∨ (Q ∧ \neg Q) ∨ (\neg P ∧ \neg Q)$ = $ P ∨ (\neg P ∧ \neg Q)$ = $ ( P ∨ \neg Q) ∧ ( P ∨ \neg Q)$ = $ ( P ∧ Q)$

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