Question

Test the validity of the argument (S₁, S₂; S), where

S₁ ; p ∨ q, S₂ : ~ p and S : q.

Answer 1

In order to test the validity of the argument (S₁, S₂ ; S), we first construct the truth table for the conditional statement.

S₁ ∧ S₂ → S i.e [(p ∨ q) ∧ ~p] → q

The truth table is as given below:

We observe that the last common of the truth table for S₁ ∧ S₂ → S contains T only. Thus, S₁ ∧ S₂ → S is a tautology.

Hence, the given argument is valid.