Proving Power Set Inclusion When B is Included in C

yxgao
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How do you show that if B is included in C, then the power set of B is included in the power set of C?
 
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What have you tried already? I'd imagine just starting with the definitions would give a strong clue.
 
Power set of C includes all subsets of C, which means that it also includes all subsets of a subset (B). Thus it includes the power set of B.
Is this formal enough?
 

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