Let Δ ∈ ∧, ∨, ⇒, Leftrightarrow be such that ( p ∧ q ) Δ(( p ∨ q ) ⇒ q ) is a tautology. Then Δ is equal to:

Question

Let Δ ∈ ∧, ∨, ⇒, Leftrightarrow be such that ( p ∧ q ) Δ(( p ∨ q ) ⇒ q ) is a tautology. Then Δ is equal to: (A) ∧ (B) ∨ (C) ⇒ (D)  Leftrightarrow

Tardigrade Admin · Accepted Answer

p ∨ q ⇒ q ⇒ ∼( p ∨ q ) ∨ q ⇒(∼ p ∧ ∼ q ) ∨ q ⇒(∼ p ∨ q ) ∧(∼ q ∨ q ) ⇒(∼ p ∨ q ) ∧ t =∼ p ∨ q Now by taking option C ( p ∧ q ) ⇒ ∼ p ∨ q ⇒ ∼ p ∨ ∼ q ∨ ∼ p ∨ q ⇒ t

Q. Let $Δ \in {\land, \lor, \Rightarrow, \Leftrightarrow}$ be such that $(p \land q) Δ ((p \lor q) \Rightarrow q)$ is a tautology. Then $Δ$ is equal to:

$\land$

$\lor$

$\Rightarrow$

$\Leftrightarrow$

Q. Let Δ∈{∧,∨,⇒,⇔} be such that (p∧q)Δ((p∨q)⇒q) is a tautology. Then Δ is equal to:

∧

∨

⇒

⇔

p∨q⇒q ⇒∼(p∨q)∨q ⇒(∼p∧∼q)∨q ⇒(∼p∨q)∧(∼q∨q) ⇒(∼p∨q)∧t=∼p∨q Now by taking option C (p∧q)⇒∼p∨q ⇒∼p∨∼q∨∼p∨q ⇒t

Q. Let $Δ \in {\land, \lor, \Rightarrow, \Leftrightarrow}$ be such that $(p \land q) Δ ((p \lor q) \Rightarrow q)$ is a tautology. Then $Δ$ is equal to:

$\land$

$\lor$

$\Rightarrow$

$\Leftrightarrow$