Question 1074891
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Let U be a universal set which contains the sets (the subsets) A and B (and relative to which we consider complements).


Let x be the element of U which belongs to {{{B^c}}}.

Then x does not belong to B, by the definition of a complement.

It implies that x does not belong to A (since A is a subset of B).

Hence, x belongs to {{{A^c}}}, by the definition of a complement.


Thus we proved that EVERY element x which belongs to {{{B^c}}} belongs to {{{A^c}}} also.


It means that {{{B^c}}} is a subset of {{{A^c}}}.


It is what has to be proved.


The proof is completed.
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The problem is solved completely.