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+7 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 Boss (40.4k points)
retagged by | 444 views
+1
A,B and C are equivalent

3 Answers

+11 votes
Best answer
  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 .

answered by Boss (20.6k points)
selected by
+5 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 (61.1k points)
edited by
0
D is not equivalent
+1
Already done
0
How D?
0
i was taken as  $\sim$(Q $\rightarrow$ P)
0
That is also not true.
+3

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

+3 votes
A) P→Q <=> ~P $\vee$ Q

       B) ¬Q→¬P <=>~(~Q) $\vee$~P <=> Q $\vee$ ~P <=> ~P $\vee$ Q         [ ~(~A)=A ]

       C) ¬P $\vee$ Q

       D) ¬Q → P <=>~(~Q) $\vee$ P <=> Q $\vee$ P

         So, You see above

         Answer is A<=>B<=>C
answered by Boss (14.4k points)
edited by

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