You're jumping ahead. is a single formula and so has a truth table which you can check by trying all four possible values for P and Q (it comes out true every time, that is, it is a tautology). In your example, P=true and Q=true we have and both true, and so the overall formula is true.

A reason why propositional calculus is interesting is that, for an appropriate set of axioms, one can show that a propositional formula is deducible if and and only if it is a tautology.

Another reason is that the implication operator "captures" the notion of deducibility in the formal system: that is, Q can be deduced from P together with the axioms, if can be deduced from the axioms alone. This is a theorem, not part of the definition -- but of course the axioms are set up so that the theorem can be proved.

So your comment