Partial truth table and proving or disproving tautology

Question

Let $p,q$ be elementry statements and $\alpha,\beta,\gamma$ be statements. (sorry if this is the wrong translation).

Prove/disprove:

1. is $p,q\Rightarrow \gamma$ tautology?

2. is $\alpha,\beta\Rightarrow \gamma$ tautology?

I think both are wrong since we have no information about the part in the red square below, for all we know $\gamma$ can be false with everything else. But it seems too easy so I'm doubting myself..

Note: $\Rightarrow$ means tautology, comma means $\wedge$.

Answer 1

1. True, since by the definition of tautology:

From wiki

A formula of propositional logic is a tautology if the formula itself is always true regardless of which valuation is used for the propositional variables

So we can see from the truth table that $p,q,\gamma$ are all true therefore it's a tautology.

2. False, take $\alpha=p\vee\neg p,\beta=q\vee\neg q, \gamma=(p\wedge q)$ so for $p=0,q=0$, $\alpha=1,\beta=1$ but $\gamma=0$ therefore it isn't tautology.

Thanks to Git Gud for the help.