Arjun Suresh (talk | contribs) |
Arjun Suresh (talk | contribs) |
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| + | Which one of the following is equivalent to $P \vee Q$? | ||
| − | (A) $\neg Q □ & | + | (A) $\neg Q □ &neg P$ |
(B) '''$P□\neg Q$''' | (B) '''$P□\neg Q$''' | ||
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==={{Template:Author|Happy Mittal|{{mittalweb}} }}=== | ==={{Template:Author|Happy Mittal|{{mittalweb}} }}=== | ||
| − | If we compare column of $ | + | 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 $P□\neg Q$. |
{{Template:FBD}} | {{Template:FBD}} | ||
[[Category: GATE2009]] | [[Category: GATE2009]] | ||
| − | [[Category: Graph Theory questions]] | + | [[Category: Graph Theory questions from GATE]] |
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) $\neg P□ \neg Q$
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 $P□\neg Q$.
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) $\neg P□ \neg Q$
If we compare column of $P\neg Q$ 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.
GATECSE