Here are $2$ circuits, the goal is to convert them to truth tables.
I'm thinking about converting them to expressions first, then making the tables.
So the first one should be $(1)$, and the second one $(2)$.
$$(xy)+(x'x') = (xy)+x'\tag{1}$$ $$(xyz)+(xx'z')+(x'yz')+(x'x'z) = xyz + x'yz' + x'z\tag{2}$$
Am I right so far?
Your expressions for the first $(1)$ and second $(2)$ circuit are correct.
$$xy+x'\tag{1}$$
$$xyz + x'yz' + x'z\tag{2}$$
Both expressions $(1,2)$ can be simplified further with a truth table or Karnaugh map, followed by the distributive law $(3,4)$.
The $1^{st}$ expression:
\begin{array}{c|cc} &x'&x\\\hline y'&\color{blue}{1}&0\\ y&\color{blue}{1},\color{red}{1}&\color{red}{1} \end{array}
$$\color{blue}{x'}+\color{red}{y}\tag{3}$$
The $2^{nd}$ expression:
\begin{array}{c|cccc} &x'y'&x'y&xy&xy'\\ \hline z'&0&\color{blue}{1}&0&0\\ z&\color{red}{1}&\color{red}{1},\color{blue}{1},\color{orange}{1}&\color{orange}{1}&0 \end{array}
$$\color{blue}{x'y}+\color{red}{x'z}+\color{orange}{yz}\tag{4}=x'(y+z)+yz$$