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18 votes
18 votes

Which of the following well-formed formulas are equivalent?

  1. $P \rightarrow Q$
  2. $\neg Q \rightarrow \neg P$
  3. $\neg P \vee Q$
  4. $\neg Q \rightarrow P$
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7 Answers

Best answer
24 votes
24 votes
  1. $P→Q   \equiv \neg P\vee Q$
  2. $¬Q→¬P\equiv Q\vee \neg P$
  3. $¬P\vee Q   \equiv \neg P \vee Q$

So, $A,B,C$ are equivalent .

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8 votes
8 votes
  1. $P\rightarrow Q \equiv \neg P \vee Q$
  2. $\neg Q\rightarrow \neg P\equiv \neg(\neg Q)\vee \neg P \equiv \neg P \vee Q$
  3. $\neg P\vee Q$
  4. $\neg Q \rightarrow P\equiv \neg (\neg Q) \vee P \equiv P \vee Q$


So,  $A,B$ and $C$ are equivalent.

edited by
7 votes
7 votes
A,B,C are equavelent i.e. $P\rightarrow Q \equiv \sim P \vee Q$

A and C are equal because if $\rightarrow$ is true then Contradiction always true.
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2 votes
2 votes

Let P and Q be statements.

1. (PQ)⇔(¬P V Q),

2. (PQ)⇔(¬Q→¬P), that is, the implication PQ is logically equivalent to the contrapositive ¬Q→¬P.

Hence 1 2 and 3 are equivalent.

Answer:

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