Arjun Suresh (talk | contribs) |
Arjun Suresh (talk | contribs) |
||
| Line 22: | Line 22: | ||
|} | |} | ||
| − | (A) $\neg Q | + | (A) $\neg Q □ ¬P$ |
| − | (B) '''$ | + | (B) '''$P□\neg Q$''' |
| − | (C) $ | + | (C) $\neg P□Q$ |
| − | (D) $ | + | (D) $\neg P□ \negQ$ |
==={{Template:Author|Happy Mittal|{{mittalweb}} }}=== | ==={{Template:Author|Happy Mittal|{{mittalweb}} }}=== | ||
| − | If we compare column of $P | + | 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>(B)</b> is correct. |
{{Template:FBD}} | {{Template:FBD}} | ||
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.
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) $P□¬Q$
(C) $¬P□Q$
(D) $¬P□¬Q$
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 $P□¬Q$, and therefore, option (B) is correct.
GATECSE