Show that if $A \subset B,$ then $C - B \subset C - A$ .

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Solution

Given: $A \subset B$
To prove: $C - B \subset C - A$
Let $x \in C$ and $x \notin B$
As $A \subset B$ , so we can conclude
$x \in C$ and $x \notin A$
$\Rightarrow x \in C - A$
So, $C - B \subset C - A$
Hence proved.

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