document.write( "Question 981563: Determine whether the following statements are true or false. Justify your answer.
\n" ); document.write( "i) A sufficient condition for an integer to be divisible by 8 is that it is divisible by 16.\r
\n" ); document.write( "\n" ); document.write( "ii) A necessary condition for an integer to be divisible by 6 is that it be divisible by 2.\r
\n" ); document.write( "\n" ); document.write( "iii) For all integers a,b, and c, if a|(b + c), then a|b or a|c \n" ); document.write( "
Algebra.Com's Answer #754784 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
Determine whether the following statements are true or false. Justify your answer.
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document.write( "\"SUFFICIENT conditions GUARANTEE!\"\r\n" );
document.write( "\"NECESSARY conditions GET GUARANTEED!\"\r\n" );
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\n" ); document.write( "i) A sufficient condition for an integer to be divisible by 8 is that it is
\n" ); document.write( "divisible by 16.
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document.write( "True, it's a SUFFICIENT condition, because it's ENOUGH information to know that\r\n" );
document.write( "an integer is divisible by 16, to be sure that it's divisible by 8.\r\n" );
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document.write( "[It's a SUFFICIENT condition to know that 48 is divisible by 16, for that's\r\n" );
document.write( "ENOUGH information to tell us that 48 is divisible by 8.  However, it's not a\r\n" );
document.write( "NECESSARY condition because, for instance, 24 is NOT divisible by 16, yet 24\r\n" );
document.write( "is divisible by 8.] \r\n" );
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\n" ); document.write( "ii) A necessary condition for an integer to be divisible by 6 is that it be
\n" ); document.write( "divisible by 2.
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document.write( "True, it's a NECESSARY condition, because we MUST KNOW that an integer is\r\n" );
document.write( "divisible by 2, i.e., that it is even, in order for it to be divisible by 6.\r\n" );
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document.write( "[It's a NECESSARY condition to know that 42 is divisible by 2, for it to be\r\n" );
document.write( "divisible by 6.  However, it's not a SUFFICIENT because 22 is divisible by 2\r\n" );
document.write( "but 22 is not divisible by 6.]\r\n" );
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\n" ); document.write( "For all integers a,b, and c, if a|(b + c), then a|b or a|c
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document.write( "That's false because 3|(7+8) but it is not true because 3|7 and 3|8 are both\r\n" );
document.write( "false.\r\n" );
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document.write( "[However \"a|b and a|c\" is a sufficient (but not necessary) condition that \r\n" );
document.write( "a|(b+c).]\r\n" );
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document.write( "Edwin
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