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. ${}\alpha \wedge \beta \rightarrow \alpha$.
3. ${}\alpha \rightarrow {\left(\beta \rightarrow \alpha \right)}$.
4. ${}{\left(\alpha \rightarrow {\left(\beta \rightarrow \gamma \right)}\right)}\rightarrow {\left({\left(\alpha \rightarrow \beta \right)}\rightarrow {\left(\alpha \rightarrow \gamma \right)}\right)}$.
5. ${}{\left(\alpha \rightarrow \beta \right)}\leftrightarrow (\neg \alpha \vee \beta )$.

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