Tautology is a very trivial rule for the following scenario:
(i) p V p; (ii) p;
Observe that disjunction does not in general allow one to detach one of the
disjuncts and assert it on its own. However, when applying Tautology, if
both disjuncts are the same propositional variable, then of course it's
valid to infer that each "one" is true "on its own." p V p is a disjunction
so, that means that at least one of the disjuncts must be true, which means
that either p (on the left) must be true, or p (on the right) must be true.
Well, in either case, p is definitely true. So this is clearly a valid move.
Tautology is a very trivial rule for the following scenario: (i) p V p; (ii) p; Observe that disjunction does not in general allow one to detach one of the disjuncts and assert it on its own. However, when applying Tautology, if both disjuncts are the same propositional variable, then of course it's valid to infer that each "one" is true "on its own."
p V pis a disjunction so, that means that at least one of the disjuncts must be true, which means that either p (on the left) must be true, or p (on the right) must be true. Well, in either case, p is definitely true. So this is clearly a valid move.