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+6 votes
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Answer the following:

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. $\neg Q \rightarrow P$
asked in Mathematical Logic by Veteran (47.8k points)
retagged by | 308 views
A,B and C are equivalent

3 Answers

+9 votes
Best answer
  1. P→Q    = P'+Q
  2. ¬Q→¬P=Q+P'
  3. ¬PVQ   =P'+Q
    so A,B,C are equivalent .
answered by Veteran (22.1k points)
selected by
+4 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.
answered by Veteran (60.4k points)
edited by
D is not equivalent
Already done
How D?
i was taken as  $\sim$(Q $\rightarrow$ P)
That is also not true.

I know that sir Or wil changes to And. thats why changed that.

+2 votes

 

  1. P→Q <=> ~P VQ
  2. ¬Q→¬P <=>~(~Q) V~P <=> Q V~P <=>~P V Q         [ ~(~A)=A ]
  3. ¬P∨Q
  4. ¬Q→P <=>~(~Q) V P <=> Q V P
  5. So You see above
  6. Answer is A<=>B<=>C
answered by Boss (6.7k points)
edited by


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