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Question

Find the correct answer 
If $$\displaystyle  A\subset C,then A\times B\subset C\times B.$$


A
True
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B
False
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Solution

The correct option is A True
Let $$x$$ be an element in A.
Then for all elements $$x\epsilon A$$, $$x\epsilon C$$ since $$A\subset C$$
Hence for every element $$x'$$ in $$A\times B$$,
$$x'\epsilon C\times B$$
Hence
$$A\times B\subset C\times B$$.

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