The number of values of r ∈ p , q , ~ p , ~ q for which p ∧ q ⇒ r ∨ q ∧ ( p ∧ r ⇒ q is a tautology, is :

Step-by-step solution

Given condition is, p ∧ q → r ∨ q ∧ p ∧ r → q ) . . . . . ( 1 ) We know conditional disjunction as, p → q ≡ ~ p ∨ q Hence, p ∧ r → q ≡ ~ p ∧ r ∨ q Using De Morgan's law p ∧ r → q ≡ ~ p ∧ r ∨ q ≡ ~ p ∨ ~ r ∨ q Equation 1 can be written as, ⇒ p ∧ q → r ∨ q ∧ ~ p ∨ ~ r ∨ q ) ⇒ ~ p ∧ q ∨ r ∨ q ∧ ~ p ∨ ~ r &#8