$S_1 : \neg p \wedge ( p \vee q ) \to q$
If consequence is false and hypothesis is true, then we will get False in the truth table.
Lets assume $q$ is false. So consequence is FALSE.
Can it make Hypothesis TRUE?
Hypothesis: $\neg p \wedge ( p \vee q ) \equiv \neg p \wedge ( p \vee \text{FALSE} ) \equiv \neg p \wedge ( p ) \equiv \text{FALSE}.$
Hypothesis can’t be true, So we can’t get False in the Truth Table.
∴ $S_1$ is Tautology.
$S_2: q \to \neg p \wedge ( p \vee q )$
If hypothesis is true and consequence is false, then we will get False in the truth table.
Lets assume $q$ is True, So Hypothesis is TRUE.
Can it make Consequence FALSE ?
Consequence: $\neg p \wedge ( p \vee q ) \equiv \neg p \wedge ( p \vee \text{TRUE} ) \equiv \neg p \wedge ( \text{TRUE} ) \equiv \neg p$
Consequence can be false and so we can get False in the Truth Table.
∴ $S_2$ is not Tautology.
Correct Option: B