In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.
If $A \subset B$ and $x \notin B,$ then $x \notin A$
In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.
If $A \subset B$ and $x \notin B,$ then $x \notin A$
True
Let $A \subset B$ and $x \notin B$
To show: $x \notin A$
If possible, suppose $x \in A$
Then, $x \in B,$ which is a contradiction as $x \notin B$
$\therefore x \notin A$
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