Prove or disprove this set equality.

The intersection $(A-C)\cap(C-B)$ is empty,

because any element of $A-C$ is not in $C$, and any element of $C-B$ is in $C$,

so there are no elements in $A-C$ and $C-B$.

J. W. Tanner's answer is correct, but just to do it via a Venn diagram:

$A - C$ is region I and region IV

$C - B$ is region III and region V

Since there are no regions in both, $(A - C)\cap(C - B)$ must empty i.e. $\emptyset$