Let Δ, nabla ∈ Lambda, V be such that ( p arrow q ) Δ( p nabla q ) is a tautology. Then

Question

Let Δ, nabla ∈ Lambda, V be such that ( p arrow q ) Δ( p nabla q ) is a tautology. Then (A) Δ=∧, nabla=∧ (B) Δ=∨, nabla=∨ (C) Δ=∨, nabla=∧ (D) Δ=∧, nabla=∨

Tardigrade Admin · Accepted Answer

Given ( p arrow q ) Δ( p nabla q ) Option I Δ=∧, nabla=∨

Hence, it is tautology. Option 4 Δ=∧, nabla=∧

Q. Let $Δ, \nabla \in {Λ, V}$ be such that $(p \to q) Δ (p \nabla q)$ is a tautology. Then

$Δ = \land, \nabla = \land$

$Δ = \lor, \nabla = \lor$

$Δ = \lor, \nabla = \land$

$Δ = \land, \nabla = \lor$

Given $(p \to q) Δ (p \nabla q)$
Option I $Δ = \land, \nabla = \lor$

Hence, it is tautology.
Option $4Δ = \land, \nabla = \land$

Q. Let Δ,∇∈{Λ,V} be such that (p→q)Δ(p∇q) is a tautology. Then

Δ=∧,∇=∧

Δ=∨,∇=∨

Δ=∨,∇=∧

Δ=∧,∇=∨