How to proof $A \times (B - C) \subseteq (A \times B) - (A \times C)$ # My attempt: Suppose $x \in A \times (B - C).$ We know x is of the form $(a, d)$, where $a \in A$ and $d \in B - C$. We know, by the definition of -, that $d \in B$ and $d \notin C$. Got stuck there and don't get how to synthetize a proof of the theorem

...where $a\in A$ and $d\in B-C$. We know by definition of $-$ that $d\in B$ and $d\
otin C$.

That is to say, $~~~a\in A$ and $d\in B~~~$ as well as $~~~a\in A$ and $d\
otin C$.

The first two imply that $(a,d)\in A\times B$ while the second two imply that $(a,d)\
otin A\times C$

These together imply that...

> $(a,d)\in (A\times B)-(A\times C)$ thus proving our desired claim.