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← JEE Main 2022 · 26 Jun · Shift 1
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JEE Main 2022 · 26 Jun · Shift 1, Mathematics question 20

Let Δ,∇∈{∧,∨}\Delta,\nabla\in\{\wedge,\vee\} be such that p ∇ q⇒((p Δ q) ∇ r)p\,\nabla\,q\Rightarrow((p\,\Delta\,q)\,\nabla\,r) is a tautology. Then (p ∇ q) Δ r(p\,\nabla\,q)\,\Delta\,r is logically equivalent to :

Choose one option
Answer and worked solution

Official answer: A

Test the four choices. Only ∇=Δ=∨\nabla=\Delta=\vee makes p∨q⇒(p∨q)∨rp\vee q\Rightarrow(p\vee q)\vee r a tautology; each other choice fails for some truth values (e.g. ∇=∨\nabla=\vee, Δ=∧\Delta=\wedge fails at p=p= T, q=r=q=r= F).

Then (p∨q)∨r≡(p∨r)∨q=(p Δ r)∨q(p\vee q)\vee r\equiv(p\vee r)\vee q=(p\,\Delta\,r)\vee q.

(A)

Topics:Mathematical reasoning
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