Filling in a missing portion of a truth table I have the following truth table:
$$
\boxed{
\begin{array}{c|c|c|c}
a &amp; b &amp; c &amp; x \\ \hline
F &amp; F &amp; F         &amp; F \\
F &amp; F &amp; T         &amp; F \\
F &amp; T &amp; F         &amp; F \\
F &amp; T &amp; T         &amp; F \\
T &amp; F &amp; F         &amp; T \\
T &amp; F &amp; T         &amp; T \\
T &amp; T &amp; F         &amp; F \\
T &amp; T &amp; T         &amp; T 
\end{array}}
$$

I am supposed to use any logical operator: and, or, not. I tried like $10$ formulas already, and I am not able to think of what combination of $a,b,c$ will get that $x$ column right. Have I missed something really silly?
$x$ is only True in rows 5, 6, and 8, all of which have $a$ as True.  This means that we should look for:

$x$ = $a$ ∧ something

Whatever that "something" is, it should return True for all combinations of $b$ and $c$ except for $b$ True and $c$ False (which was row 7, where $x$ is False).
Hint: 


   $$x\equiv a\land(\neg b\lor c).$$


How did I come up with this? Well, if $a$ is false, then any conjunction with $a\land(\text{something here})$ will be false as well. That takes care of the top half of the truth table. All that is left, then, is to figure out how to manipulate a combination of $b$ and $c$ to combine with $a$ to give the desired truth values. Thus, what you want is what is given above (grayed out in case you want to try to deduce it yourself).