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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 Boss (18k points)
edited by | 973 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 (342k points)
selected by
0
Good Explanations sir
+2
When in confusion, better to use truth table, surely to give correct answer
–1 vote
(PVQ)-->R means (PVR)-->(QVR)

equivalent( A )
answered by Active (2.7k points)
0
X -> Y?
+1
sorry X->Y will be the answer
0
they are coming equivalent ?
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