In each of the following,determine whether the statement is true or false. If it is true,prove it. If it is false,give a counterexample.
If $x \in A$ and $A \not\subset B$,then $x \in B$
If $x \in A$ and $A \not\subset B$,then $x \in B$
(N/A) The statement is $False$.
To disprove the statement,we provide a counterexample.
Let $A = \{1, 2\}$ and $B = \{1, 3\}$.
Here,$A \not\subset B$ because $2 \in A$ but $2 \notin B$.
Let $x = 2$. Then $x \in A$ and $A \not\subset B$ are satisfied.
However,$x \notin B$ because $2 \notin \{1, 3\}$.
Thus,the statement is $False$.
To disprove the statement,we provide a counterexample.
Let $A = \{1, 2\}$ and $B = \{1, 3\}$.
Here,$A \not\subset B$ because $2 \in A$ but $2 \notin B$.
Let $x = 2$. Then $x \in A$ and $A \not\subset B$ are satisfied.
However,$x \notin B$ because $2 \notin \{1, 3\}$.
Thus,the statement is $False$.
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