document.write( "Question 1166867: Let Ω ={ω∈Z|ω= 8x+ 1, for some x∈Z} and A={α∈Z|α= 8y−7, for some y∈Z}. Using element argument, prove that Ω =A \n" ); document.write( "

Algebra.Com's Answer #791417 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "It can be justified differently.\r
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document.write( "One way is to notice that both sets represent all integer numbers that give the remainder 1 when are divided by 8.\r\n" );
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document.write( "The other way is to notice that \r\n" );
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document.write( "    if  ω = 8x+1 belongs to one set, then the same number \r\n" );
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document.write( "        ω = 8x+1 = 8*(x+1)-7 belongs to the other set,\r\n" );
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document.write( "    and vice versa.\r\n" );
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document.write( "It means that the two sets COINCIDE.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, completed and explained.\r
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\n" ); document.write( "\n" ); document.write( "I an in waiting mode expecting to get your \"THANKS\" as soon as you complete reading my response.\r
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