Set Operation $D = (A \times B) - (B \times C)$ I want to find
$$
D = (A \times B) - (B \times C)
$$
where
$$
A = \{x.y,z\}, \ B = \{1,2\}, \ C = \{x,z\} 
$$
So far I have computed
$$
A \times B = \{(x,1), (x,2), (y,1),(y,2),(z,1),(z,2)\} 
$$
and
$$
B \times C = \{(1,x),(1,z),(2,x),(2,z)\} 
$$
Hence
$$
D = \{(x,1), (x,2), (y,1),(y,2),(z,1),(z,2)\} - \{(1,x),(1,z),(2,x),(2,z)\}
$$
This is where I am stuck because cartesian product order matters. The answer is
$$
D = \{(x,1), (x,2), (y,1),(y,2),(z,1),(z,2)\} 
$$
and I have no idea why. Is difference sets when set doesn't share something together like example $\{1,2,3\} - \{2,3,4\} = \{1\}$ if I am not mistaken.

Because no element of $B \times C$ is an element of $A \times B$, the set $D$ is just $A \times B$. Remember: $X - Y = \{ x \in X : x \notin Y \}$ so if every element of $X$ is not an element of $Y$ then $x \notin Y$ is always satisfied so $X - Y = \{x \in X\} = X$.
