I have a truth table as follows
X Y Z A B C
0 0 0 0 0 1
0 0 1 0 1 0
0 1 0 1 0 1
0 1 1 1 0 0
1 0 0 0 1 1
1 0 1 1 0 0
1 1 0 1 0 1
1 1 1 1 1 0
where x, y and z are inputs and a, b and c are outputs. Normally, simplifying this into an expression would be easy with one output. I would just use k-maps and get the simplified Boolean expression from it. But with three outputs, I don't know how.
It's pretty clear by inspection that $c = \neg z$, so we can get that out of the way.
The simplest way I can see to specify $a$ is that $a = y \vee (x \wedge z)$. Again by inspection.
$b$ has no simple expression that I can see; you're not doing much better than just saying "x and not y and not z, or z and not y and not x, or x and y and z".