Project ForgeDiscrete Mathematics
Propositional Logic
GATE 2016
Medium
Consider the following expressions: (i) false (ii) Q (iii) true (iv) P ∨ Q (v) ¬Q ∨ P
The number of expressions given above that are logically implied by P ∧ (P ⇒ Q) is ____.
4
Explanation
P ∧ (P⇒Q) forces both P and Q to be TRUE (by modus ponens, P and P⇒Q together give Q). Check each expression under P=Q=TRUE: (i) false — FALSE, not implied. (ii) Q — TRUE, implied. (iii) true — always TRUE, implied. (iv) P∨Q — TRUE, implied. (v) ¬Q∨P — TRUE (since P is TRUE), implied. So 4 of the 5 expressions (all except 'false') are implied.
Source: GATE CS 2016 (Session 2 / Set B) (2016)
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