Propositional logic/Tautology/Truth table/Exercise

Prove, with the help of truth tables, that the following statements are tautologies.

1. $(\alpha \wedge \alpha )\leftrightarrow \alpha$.
2. $\alpha \wedge \beta \to \alpha$.
3. $\alpha \to (\beta \to \alpha )$.
4. $(\alpha \to (\beta \to \gamma ))\to ((\alpha \to \beta )\to (\alpha \to \gamma ))$.
5. $(\alpha \to \beta )\leftrightarrow (\mathrm{\neg }\alpha \vee \beta )$.

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