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<b>(A) </b>&not;Q&#9633&not;P
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&nbsp;
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<b>(B) </b>P&#9633&not;Q
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&nbsp;
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<b>(C) </b>&not;P&#9633Q
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<b>(D) </b>&not;P&#9633&not;Q
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==={{Template:Author|Happy Mittal|{{mittalweb}} }}===
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If we compare column of $P&#9633;Q$ in table with $P &or; Q$, we need both $F$ in $3^{rd}$ row of table, and for that we need
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$&not;Q$ instead of $Q$. So $P &or; Q$ is equivalent to $P&#9633&not;Q$, and therefore, option <b>(B)</b> is correct.
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{{Template:FBD}}
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[[Category: GATE2009]]
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[[Category: Graph Theory questions]]

Revision as of 19:41, 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

(A) ¬Q&#9633¬P   (B) P&#9633¬Q   (C) ¬P&#9633Q   (D) ¬P&#9633¬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 $¬Q$ instead of $Q$. So $P ∨ Q$ is equivalent to $P&#9633¬Q$, 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) ¬Q&#9633¬P   (B) P&#9633¬Q   (C) ¬P&#9633Q   (D) ¬P&#9633¬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 $¬Q$ instead of $Q$. So $P ∨ Q$ is equivalent to $P&#9633¬Q$, and therefore, option (B) is correct.




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