The Gateway to Computer Science Excellence
+19 votes

The binary operation $\Box$ is defined as follows

$$\begin{array}{|c|c|c|} \hline \textbf{P} & \textbf{Q} & \textbf{P} \Box \textbf{Q}\\\hline \text{T} & \text{T}& \text{T}\\\hline \text{T} & \text{F}& \text{T} \\\hline \text{F} & \text{T}& \text{F}\\\hline \text{F} & \text{F}& \text{T} \\\hline \end{array}$$

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

  1.    $\neg Q \Box \neg P$
  2.    $P\Box \neg Q$
  3.    $\neg P\Box Q$
  4.    $\neg P\Box \neg Q$
in Mathematical Logic by Boss (17.5k points)
edited by | 2.2k views
Hint --> Just obtain Sum of Product expression from there answer becomes trivial.

Yes it is very easy

Thanks @Chhotu sir

4 Answers

+26 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 $\bar{ \bar{Q}}+P = P + Q$
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.
+4 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

by Loyal (8k points)
+2 votes
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.
by Boss (19.9k 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.
0 votes

From the truth table we can get that $P\;\square\;Q\;is \;Q\rightarrow P$. So the options will be-

A.  $\neg P\rightarrow\neg Q\equiv\;\neg(\neg P)\vee\neg Q\;\equiv P\vee\neg Q$    $(\because P\rightarrow Q\equiv \neg P\vee Q)$

B.  $\neg Q\rightarrow P\;\equiv\;\neg(\neg Q)\vee P\;\equiv\;$ $P\vee Q$  (correct option)


by Boss (13.1k points)

Related questions

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
50,737 questions
57,370 answers
105,274 users