Do the premises logically imply the conclusion? $$b\rightarrow a,\lnot c\rightarrow\lnot a\models\lnot(b\land \lnot c)$$
I have generated an 8 row truth table, separating it into $b\rightarrow a$, $\lnot c\rightarrow\lnot a$ and $\lnot (b\land\lnot c)$. I know that if it was 
$$\lnot c\rightarrow\lnot a\models\lnot(a \land \lnot c)$$
I would only need to check the right side with  every value that makes the left side true to make sure the overall statement is true. How do I deal with more than one premise?

The second premise $\neg c\to\neg a$ implies that $a\to c$.
The first premise $b\to a$ leads to $b\to a\to c$, which implies $\neg c\to\neg b$.
The two last statements clearly prevent $b\land\neg c$ from being true.
