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1 votes
1 votes

Let $P$ and $Q$ be two propositions $\neg (P \leftrightarrow Q)$ is equivalent to

  1. $P\leftrightarrow \neg Q$
  2. $\neg P\leftrightarrow Q$
  3. $\neg P \leftrightarrow \neg Q$
  4. $Q\rightarrow P$
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6 Answers

Best answer
2 votes
2 votes
P Q $\sim p$ $\sim Q$ $Q \rightarrow P$ $\sim(P \leftrightarrow Q)$ $P \leftrightarrow \sim Q$
$\sim P \leftrightarrow Q$
$\sim P \leftrightarrow \sim Q$
0 0 1 1 1 0 0 0 1
0 1 1 0 0 1 1 1 0
1 0 0 1 1 1 1 1 0
1 1 0 0 1 0 0 0 1

Both option(1)and (2) is the correct choice.

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3 votes
3 votes

$¬(P\leftrightarrow Q)$

$ ¬(P\rightarrow Q \wedge Q\rightarrow P)$

$¬ ((\bar{P}\vee Q) \wedge (\bar{Q}\vee P))$

$¬(\bar{P}\bar{Q} \vee PQ)$

$¬(P \odot Q)$

$(P\oplus Q)$

now check which options looks like XOR 

P $\bar{P}$ Q $\bar{Q}$ $\bar{P} \leftrightarrow Q$ $P \leftrightarrow \bar{Q}$
T F T F F F
T F F T T T
F T T F T T
F T F T F F

$\bar{P} \leftrightarrow Q$ and $P \leftrightarrow \bar{Q}$ both are correct

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