The maximum number of compound propositions, out of p ∨ r ∨ s , p ∨ r ∨ ~ s , p ∨ ~ q ∨ s , ~ p ∨ ~ r ∨ s , ~ p ∨ ~ r ∨ ~ s , ~ p ∨ q ∨ ~ s , q ∨ r ∨ ~ s , q ∨ ~ r ∨ ~ s , ~ p ∨ ~ q ∨ ~ s that can be made simultaneously true by an assignment of the truth values to p , q , r and s , is equal to

Step-by-step solution

If we take p q r s F F T F Put all the above truth value and check, p ∨ r ∨ s ⇒ True , p ∨ r ∨ ~ s ⇒ True p ∨ ~ q ∨ s ⇒ True ~ p ∨ ~ r ∨ s ⇒ True ~ p ∨ ~ r ∨ ~ s ⇒ True ~ p ∨ q ∨ ~ s ⇒ True q ∨ r ∨ ~ s ⇒ True q ∨ ~ r ∨ ~ s ⇒ True ~ p ∨ ~ q ∨ ~ s ⇒ True We can see the truth value of all the propositions will is true, so total 9