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Which one of the following is equivalent to $P ∨ Q$?
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Which one of the following is equivalent to $P \vee Q$?
  
(A) $\neg Q □ ¬P$
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(A) $\neg Q □ &neg P$
  
 
(B) '''$P□\neg Q$'''
 
(B) '''$P□\neg Q$'''
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[[Category: GATE2009]]
 
[[Category: GATE2009]]
[[Category: Graph Theory questions]]
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[[Category: Graph Theory questions from GATE]]

Latest revision as of 20:50, 15 September 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 $P \vee Q$?

(A) $\neg Q □ &neg P$

(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 T in $3^{rd}$ row of table and F in the fourth row, and for that we need $\neg Q$ instead of $Q$. So $P ∨ Q$ is equivalent to $P□\neg Q$.




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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

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[edit]

If we compare column of $P□ Q$ in table with $P ∨ Q$, we need T in $3^{rd}$ row of table and F in the fourth row, and for that we need $\neg Q$ instead of $Q$. So $P ∨ Q$ is equivalent to $P□\neg Q$.




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