Project ForgeDiscrete Mathematics
Propositional Logic
GATE 2009
Hard
The binary operation □ is defined as follows: P□Q is T,T,F,T for (P,Q) = (T,T),(T,F),(F,T),(F,F) respectively. Which one of the following is equivalent to P ∨ Q?
- A¬Q □ ¬P
- P □ ¬Q
- C¬P □ Q
- D¬P □ ¬Q
Explanation
Testing P□(¬Q) against every row: P=T,Q=T→¬Q=F, T□F=T (from the table), matches P∨Q=T. P=T,Q=F→¬Q=T, T□T=T, matches P∨Q=T. P=F,Q=T→¬Q=F, F□F=T, matches P∨Q=T. P=F,Q=F→¬Q=T, F□T=F, matches P∨Q=F. All four rows match, so P□¬Q ≡ P∨Q.
Source: GATE CS 2009 (2009)
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