Question

For any two sets A and B, prove that: .

Answer 1

Let $a\in A\Rightarrow a\notin B\left(\because A\cap B=\varphi \right)$.

$\Rightarrow a\in B\text{'}$

Thus, $a\in A\mathrm{and}a\in B\text{'}\Rightarrow A\subseteq B\text{'}$.