Let Δ , ∇ ∈ ∧ , ∨ be such that p ∇ q → p Δ q ∇ r is a tautology. Then p ∇ q ∆ r is logically equivalent to

Question

Let Δ , ∇ ∈ ∧ , ∨ be such that p ∇ q → p Δ q ∇ r is a tautology. Then p ∇ q ∆ r is logically equivalent to, p Δ r ∨ q, p Δ r ∧ q, p ∧ r Δ q, p ∇ r ∧ q

MARKS App · Accepted Answer

Case-I If Δ ≡ ∇ ≡ ∧ p ∧ q → p ∧ q ∧ r then it is false if r is false. So not a tautology Case-II If Δ ≡ ∇ ≡ ∨ p ∨ q → p ∨ q ∨ r ≡ tautology then p ∨ q ∨ r ≡ p Δ r ∨ q Case-III If Δ = ∨ , ∇ = ∧ then p ∧ q → p ∨ q ∧ r is not a tautology when p → T , q → T , r → F Case-IV If Δ = ∧ , ∇ = ∨ p ∧ q → p ∧ q ∨ r is not a tautology

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