document.write( "Question 344425: If set S consists of all odd multiples of 3, that is, S = (…,‐9, ‐3, 3, 9,…). If the integers x and y are in S, which of the following must also be in S?\r
\n" ); document.write( "\n" ); document.write( "(a) xy (b) x+y (c) x-y (d) x/y (e) -x-y \n" ); document.write( "

Algebra.Com's Answer #246357 by Fombitz(32388) $\"\"$ $\"About$

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Let $\"x=3n\"$ and $\"y=3m\"$ , where $\"n\"$ and $\"m\"$ are odd integers.
\n" ); document.write( "a) $\"xy=9nm\"$ , which is also an odd multiple of $\"3\"$ since two odd integers multiplied together produce an odd integer.
\n" ); document.write( "b) $\"x%2By=3n%2B3m=3%28n%2Bm%29\"$ which is a even multiple of $\"3\"$ since two odd integers add to an even integer. Then an even 3 times an even integer is even.
\n" ); document.write( "c) $\"x-y=3n-3m=3%28n-m%29\"$ which is a even multiple of $\"3\"$ like b.
\n" ); document.write( "d) $\"x%2Fy=%283n%29%2F%283m%29=n%2Fm\"$ , which may or may not be a multiple of $\"3\"$ .
\n" ); document.write( "e) $\"-x-y=-3n-3m=-3%28n%2Bm%29\"$ , which is a even multple of $\"3\"$ like b.
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\n" ); document.write( "Only a) is included in S.
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