document.write( "Question 1074891: determine whether it is valid or invalid. If valid then give a proof. If invalid then give a counter example.
\n" ); document.write( "A⊆B ⇒(B)^c⊆(A)^c. Where ()^c means complement. \n" ); document.write( "

Algebra.Com's Answer #689732 by ikleyn(52909) $\"\"$ $\"About$

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document.write( "Let U be a universal set which contains the sets (the subsets) A and B (and relative to which we consider complements).\r\n" );
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document.write( "Let x be the element of U which belongs to .\r\n" );
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document.write( "Then x does not belong to B, by the definition of a complement.\r\n" );
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document.write( "It implies that x does not belong to A (since A is a subset of B).\r\n" );
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document.write( "Hence, x belongs to , by the definition of a complement.\r\n" );
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document.write( "Thus we proved that EVERY element x which belongs to  belongs to  also.\r\n" );
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document.write( "It means that  is a subset of .\r\n" );
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document.write( "It is what has to be proved.\r\n" );
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document.write( "The proof is completed.\r\n" );
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