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Which one of the following is equivalent to $P ∨ Q$?
 
(A) $\neg Q □ ¬P$
 
(A) $\neg Q □ ¬P$
  

Revision as of 19:49, 14 July 2014

The binary operation □ is defined as follows

$P$ $Q$ $P□Q$
T T T
T F T
F T F
F F T

Which one of the following is equivalent to $P ∨ Q$? (A) $\neg Q □ ¬P$

(B) $P□\neg Q$

(C) $\neg P□Q$

(D) $\neg P□ \neg Q$

Solution by Happy Mittal

If we compare column of $P□ Q$ in table with $P ∨ Q$, we need both F in $3^{rd}$ row of table, and for that we need $\negQ$ instead of $Q$. So $P ∨ Q$ is equivalent to $P□\negQ$, and therefore, option (B) is correct.




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The binary operation □ is defined as follows

$P$ $Q$ $P□Q$
T T T
T F T
F T F
F F T

(A) $\neg Q □ ¬P$

(B) $P□\neg Q$

(C) $\neg P□Q$

(D) $\neg P□ \neg Q$

Solution by Happy Mittal[edit]

If we compare column of $P□ Q$ in table with $P ∨ Q$, we need both F in $3^{rd}$ row of table, and for that we need $\negQ$ instead of $Q$. So $P ∨ Q$ is equivalent to $P□\negQ$, and therefore, option (B) is correct.




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