I'm totally new to predicate logic and I need to determine if following formulas are tautology or not.
I can clearly see that first formula tautology is, but how could I check it for the others?
$$\begin{align} \alpha ~&=~ \forall x~\big(P(x) \vee \neg P(x)\big) \\[2ex]\beta ~&=~ \big(\forall x~P(x)\big) \vee \big(\forall x~\neg P(x)\big) \\[2ex]\gamma ~&=~ \big(\forall x~P(x)\big) \vee \big(\exists x~\neg P(x)\big) \end{align}$$