Arjun Suresh (talk | contribs) |
Arjun Suresh (talk | contribs) |
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The binary operation □ is defined as follows | The binary operation □ is defined as follows | ||
{| class="wikitable" | {| class="wikitable" | ||
| − | ! P | + | ! $P$ |
| − | ! Q | + | ! $Q$ |
| − | ! P□Q | + | ! $P□Q$ |
|- | |- | ||
| T | | T | ||
| Line 28: | Line 28: | ||
(C) $\neg P□Q$ | (C) $\neg P□Q$ | ||
| − | (D) $\neg P□ \ | + | (D) $\neg P□ \neg Q$ |
==={{Template:Author|Happy Mittal|{{mittalweb}} }}=== | ==={{Template:Author|Happy Mittal|{{mittalweb}} }}=== | ||
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.
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) $\neg P□ \negQ$
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