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\n" ); document.write( "Multiples of 12 are a subset of the multiples of n
\n" ); document.write( "What must be true about n?
\n" ); document.write( "a- 12<= n
\n" ); document.write( "b- n<= 12
\n" ); document.write( "c- 12|n
\n" ); document.write( "d- n|12
\n" ); document.write( "e- n and 12 are relative prime.
\n" ); document.write( "I think n<=12 , and n|12
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document.write( "In this problem, we have two subsets of integer numbers.\r\n" );
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document.write( "One subset, let's call it T, is the subset of multiples of 12: T = {12, 24, 36, . . . }.\r\n" );
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document.write( "Another subset, let's call it N, is the subset of multiples of n: N = {n, 2n, 3n, . . . }.\r\n" );
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document.write( "We are given that T is subset of N, or, in other words, every number of T, i.e. a number \r\n" );
document.write( "of the form 12k, is the element of N: 12k = m*n for some m.\r\n" );
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document.write( "In particular, the number of 12 is the element of T, i.e. 12 = m*n for some integer m.\r\n" );
document.write( "It means that n is a divisor of 12, or n|12.\r\n" );
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document.write( "ANSWER. Both conditions, (b) and (d), must be satisfied.\r\n" );
document.write( "\r\n" ); document.write( "\n" ); document.write( "Solved and explained.\r
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