I've figured out that \(X = \bar{A}BC + A\bar{B}C + AB\bar{C}\)

Now I want to set up the truth table, but I'm unsure how to do that when there are three variables instead of two. Can you help me?

 

With 3 inputs you have 8 different possibilities (2^3). Start from 000, then 001, then 010 and so on up to 111 (binary counting). Apply each possibility to your boolean equation and find X.

 

How do I calculate 1*1*1, 1*0*1 + 0*0*1 etc?

 

A'BC has to take an input of 011 as for the AND gate to output a 1. You need to have 0 logic for inverting inputs as to be taken as 1 from the AND gate.