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+14 votes
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
asked in Mathematical Logic by Veteran (18k points)
edited by | 893 views

2 Answers

+21 votes
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 by Veteran (346k points)
selected by
Good Explanations sir
When in confusion, better to use truth table, surely to give correct answer
–1 vote
(PVQ)-->R means (PVR)-->(QVR)

equivalent( A )
answered by Loyal (2.8k points)
X -> Y?
sorry X->Y will be the answer
they are coming equivalent ?

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