If A, B, C are three sets such that A , then prove that C - B - A… - Vidyadip

Question

If A, B, C are three sets such that $\text{A}\subset\text{B},$ then prove that $\text{C} - \text{B}\subset\text{C} - \text{A}.$

✓

Answer

We have, ACB
To show: $\text{C} - \text{B}\subset\text{C} - \text{A}$
Let, $\text{x}\in\text{C} - \text{B}$
$\Rightarrow\text{x} \in \text{C and x}\not\in\text{B}$
$\Rightarrow\text{x} \in \text{C and x}\not\in\text{A}$ $[\because \text{A} \subset \text{B}]$
Thus, $\text{x} \in \text{C} - \text{B}\Rightarrow\text{x}\in \text{C} - \text{A}$
This is true for all $\text{x}\in\text{C} - \text{B}$
$\therefore \text{C} - \text{B} \subset \text{C} - \text{A}.$

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