Question

Show that if $A ⊂ B$, then $C – B ⊂ C – A.$

Answer 1

Let $A ⊂ B$
To show: $C – B ⊂ C – A$
Let $x ∈ C – B$
$⇒ x ∈ C$ and $x ∉ B$
$⇒ x ∈ C$ and $x ∉ A [A ⊂ B]$
$⇒ x ∈ C – A$
$∴ C – B ⊂ C – A$