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+14 votes

The binary operation □ is defined as follows


P Q P □ Q

Which one of the following is equivalent to $P \vee Q$?

  1.    $\neg Q □ \neg P$
  2.    $P□\neg Q$
  3.    $\neg P□Q$
  4.    $\neg P□ \neg Q$
asked in Mathematical Logic by Veteran (19.6k points)
edited by | 1.1k views
Hint --> Just obtain Sum of Product expression from there answer becomes trivial.

Yes it is very easy

Thanks @Chhotu sir

3 Answers

+21 votes
Best answer
Answer is B because the truth values for option B is same as that of P "or" Q.

The given truth table is for $Q \implies P$ which is $\bar Q+P$.

Now, with A option we get $\bar{ \bar{Q}}+P = P + Q$
answered by (383 points)
selected by
(a) option is Q' + P which is false

(b) is right one

Yes @NItin answer is b) . It can be solved by doing mapping and then using implication as P□ Q = Q---->p 

@Arjun Sir please explain the question ?
ans is 'c' ,    given operation in the truth table is implication ,  Q---->P .    option c is equivalent to P+Q.
Hello set2018

Question is , there is some operator $\square$ , for which truth table is given , like when first operand is T and second operand is T , o/p will be T. When first operand is T and second is F , o/p will be so just on the bases of this truth table , you have to find truth tabes for Q'$\square$P' , P$\square$Q' , P'$\square$Q , P'$\square$Q' ,now compare those truth tables with truth table for P∨Q , see which one exactly matches with that one.
+3 votes

Here (P □ Q ) is equivalent to (Q-->P) so by this (P v Q) is equivalent to (P□¬Q).

So the ans is (B) P□¬Q


answered by Veteran (16.4k points)
+1 vote
The answer will be A.

The given truth table is of the form P ⇐ Q which is Q'+P.

and option A satisfies that as Q' ⇐ P' is Q' + P.
answered by Veteran (19.8k points)
Answer is C as □ is equal to implication .On applying implication in C we get P or Q.
We have to find P V Q.

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