Line 1: Line 1:
 
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) $\neg P□ \negQ$
+
(D) $\neg P□ \neg Q$
 
==={{Template:Author|Happy Mittal|{{mittalweb}} }}===
 
==={{Template:Author|Happy Mittal|{{mittalweb}} }}===
  

Revision as of 19:47, 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) $\neg Q □ ¬P$

(B) $P□\neg Q$

(C) $\neg P□Q$

(D) $\neg P□ \neg Q$

Solution by Happy Mittal

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.




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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) $\neg Q □ ¬P$

(B) $P□\neg Q$

(C) $\neg P□Q$

(D) $\neg P□ \negQ$

Solution by Happy Mittal[edit]

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.




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