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

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Solution

Let $x \in C - B \Rightarrow x \in C$ and $x \notin B$

$\Rightarrow x \in C$ and $x \notin A$ $[∵ A \subset B]$

$\Rightarrow x \in C - A$

Hence $C - B \subset C - A .$

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