Question

The conditional statement ((p ∧ q) `rightarrow` ((∼p) ∨ r)) v (((∼p) ∨ r) `rightarrow` (p ∧ q)) is ______.

Options

• a tautology

• a contradiction

• equivalent to p ∧ q

• equivalent to (∼p) ∨ r

Answer 1

The conditional statement ((p ∧ q) `rightarrow` ((∼p) ∨ r)) v (((∼p) ∨ r) `rightarrow` (p ∧ q)) is a tautology.

Explanation:

Given conditional statement is

((p ∧ q) `rightarrow` ((∼p) ∨ r)) v (((∼p) ∨ r) `rightarrow` (p ∧ q))

⇒ Here, (A `rightarrow` B) is equal to (∼A ∨ B)

From given statement,

⇒ (∼p ∨∼q) ∨ (∼p ∨ r) ∨ (p ∧ q)

⇒ ∼p ∨ (r ∨∼q) ∨ p(∧(∼r ∨ q))

If negation of p and only p is present with the union, then it represents tautology.