The proposition (p arrow ∼ p) ∧ (∼ p arrow p) is a

Question

The proposition (p arrow ∼ p) ∧ (∼ p arrow p) is a (A) Tautology (B) Contradiction (C) Neither a tautology nor a contradiction (D) Tautology and contradiction

Tardigrade Admin · Accepted Answer

We have, p arrow ∼ p ≅ ∼ p ∨ ∼ ≅ ∼ p and ∼ p arrow p ≅ p ∨ p ≅ p ∴ (p arrow ∼ p) ∧ (∼ p arrow p) ≅ ∼ p ∧ p≅ c

Q. The proposition $(p \to\sim p) \land (\sim p \to p)$ is a

Tautology

Contradiction

Neither a tautology nor a contradiction

Tautology and contradiction

We have,
$p \to\sim p ≅\sim p \lor \sim≅\sim p$ and $\sim p \to p ≅ p \lor p ≅ p$
$∴ (p \to\sim p) \land (\sim p \to p) ≅\sim p \land p ≅ c$

Q. The proposition (p→∼p)∧(∼p→p) is a