For any two sets of A and B, prove that: B' ' . - Vidyadip

Question

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

$\text{B}'\subset\text{A}'\Rightarrow\text{A}\subset\text{B.}$

✓

Answer

We have $\text{B}'\subset\text{A}'$
To show: $\text{A}\subset\text{B}$
Let, $\text{x}\in\text{A}$
$\Rightarrow\text{x}\not\in\text{A}'$ $[\because\text{A}\cap\text{A}'=\phi]$
$\Rightarrow\text{x}\not\in\text{B}'$ $[\because\text{B}'\subset\text{A}']$
$\Rightarrow\text{x}\in\text{B}$ $[\because\text{B}\cap\text{B}'=\phi]$
Thus, $\text{x}\in\text{A}\Rightarrow\text{x}\in\text{B}$
This is true foe all $\text{x}\in\text{A}$
$\therefore\text{ A}\subset\text{B}.$

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