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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 (29.5k points)   | 124 views
A,B and C are equivalent

3 Answers

+3 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 (20.3k points)  
selected by
0 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 (47.4k 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.

0 votes

 

  1. P→Q <=> ~P VQ
  2. ¬Q→¬P <=>~(~Q) V~P <=> QV~P <=>~PVQ         [ ~(~A)=A ]
  3. ¬P∨Q
  4. ¬Q→P <=>~(~Q)VP <=>QVP
  5. So You see above
  6. Answer is A<=>B<=>C
answered by Junior (535 points)  


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