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GATE200540
+14
votes
893
views
Let P, Q and R be three atomic propositional assertions. Let X denote ( P ∨ Q ) → R and Y denote (P → R) ∨ (Q → R). Which one of the following is a tautology?
(A) X ≡ Y
(B) X → Y
(C) Y → X
(D) ¬Y → X
gate2005
mathematicallogic
propositionallogic
normal
asked
Sep 21, 2014
in
Mathematical Logic
by
gatecse
Veteran
(
18k
points)
edited
Jan 4
by
Puja Mishra

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2
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+21
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Best answer
X = (P ⋁ Q) → R
= ~(P ⋁ Q) ⋁ R
= (~P ⋀ ~Q) ⋁ R
= (~P ⋁ R) ⋀ (~Q ⋁ R)
= (P → R) ⋀ (Q → R)
So, X → Y is true as (A ⋀ B) → (A ⋁ B) is always TRUE but reverse implication is not always true.
Hence, B.
answered
Jan 8, 2015
by
Arjun
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346k
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selected
May 3, 2015
by
Arjun
comment
Good Explanations sir
When in confusion, better to use truth table, surely to give correct answer
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–1
vote
(PVQ)>R means (PVR)>(QVR)
equivalent( A )
answered
Dec 25, 2014
by
Manali Sikdar
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2.8k
points)
comment
X > Y?
sorry X>Y will be the answer
they are coming equivalent ?
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