Question

Prove: If C⊂A and D⊂B then D−A⊂B−C

Answer 1

Let $x\in D\setminus A$, so that $x\in D$ but $x\not\in A$. Since $D\subset B$, it follows that $x\in B$, and since $C\subset A$, it follows that $x\not\in C$, which means $x\in B\setminus C$.