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Let A and B be sets. Prove that: A X {1} ( b X {1}, THEN A ( B


label Algebra
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Proceed to show the subset relation A ( B holds. 

Feb 6th, 2015

Use the negative proof:

Suppose A ( B don't hold, this is true if and only if there exist (at least one) element of A (denote it a0), which is not in B.

But in such a case the pair (a0,1) do not belongs to B X {1} (by definition of set's X).

Which, in turn, true if and only if  A X {1}   not (  B X {1}. This is a contradiction, so our assumption that A not ( B is false, so A ( B.


Feb 6th, 2015

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Feb 6th, 2015
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