Let the operations *, odot ∈ ∧, ∨ . If (p * q) odot(p odot ∼ q) is a tautology, then the ordered pair (*, odot) is :

Question

Let the operations *, odot ∈ ∧, ∨ . If (p * q) odot(p odot ∼ q) is a tautology, then the ordered pair (*, odot) is : (A) (∨, ∧) (B) (∨, ∨) (C) (∧, ∧) (D) (∧, ∨)

Tardigrade Admin · Accepted Answer

Well check each option For A π= operatornamevof 0= Lambda ( pvq ) ∧( pv ∼ q ) ≡ pv ( q ∧ ∼ q ) ≡ pv ( c ) ≡ p For B: * =v, O=v ( pvq ) ∨( pv ∼ q ) ≡ t using Venn Diagrams

Q. Let the operations $, ⊙ \in {\land, \lor}$ . If $(p q) ⊙ (p ⊙ \sim q)$ is a tautology, then the ordered pair $(*, ⊙)$ is :

$(\lor, \land)$

$(\lor, \lor)$

$(\land, \land)$

$(\land, \lor)$

Well check each option
For A $π = vof 0 = Λ$
$(p v q) \land (p v \sim q)$
$\equiv p v (q \land \sim q)$
$\equiv p v (c) \equiv p$
For $B : * = v, O = v$
$(p v q) \lor (p v \sim q) \equiv t$ using Venn Diagrams

Q. Let the operations ∗,⊙∈{∧,∨}. If (p∗q)⊙(p⊙∼q) is a tautology, then the ordered pair (∗,⊙) is :

(∨,∧)

(∨,∨)

(∧,∧)

(∧,∨)