Arjun Suresh (talk | contribs) |
Arjun Suresh (talk | contribs) |
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| − | + | (A) $¬Q□¬P$ | |
| − | + | ||
| − | + | (B) '''$P□¬Q$''' | |
| − | + | ||
| − | + | (C) $¬P□Q$ | |
| − | + | ||
| − | + | (D) $¬P□¬Q$ | |
==={{Template:Author|Happy Mittal|{{mittalweb}} }}=== | ==={{Template:Author|Happy Mittal|{{mittalweb}} }}=== | ||
| − | If we compare column of $P□Q$ in table with $P ∨ Q$, we need both | + | 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>(B)</b> is correct. | $¬Q$ instead of $Q$. So $P ∨ Q$ is equivalent to $P□¬Q$, and therefore, option <b>(B)</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) $¬Q□¬P$
(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.
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□¬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