I would like clarification on a set theory question I have.

The question reads:

Suppose $X$, $Y$ and $Z$ are sets: Does $X \times (Y +Z)=(X\times Y)+(X\times Z)$ (Where $\times$ is the cartesian product operator)?

Now, the answer is already given as:

$$X \times (Y+Z) = \{(x,(y,0))\mid x \in X, y \in Y\} \cup \{(x, (z,1)) \mid x \in X, z \in Z\}$$

$$(X \times Y) + (X \times Z) = \{((x,y),0) \mid x \in X, y \in Y\}\cup \{((x,z),1) \mid x \in X, z \in Z\}$$

I can see that by the rule of ordered pairs, these 2 sets are different. What I don't understand is where the union comes from and moreover the appearance of 0 & 1 in both of these sets? I believe it may be as simple as being unable to find clarification for what the '+' operator means, but any help with this is appreciated.

Many thanks.