document.write( "Question 685786: Determine if the set is closed for the given operation.
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Algebra.Com's Answer #424581 by Edwin McCravy(20060)\"\" \"About 
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document.write( "Determine if the set is closed for the given operation. \r\n" );
document.write( "a. the set of integers for multiplication.\r\n" );
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document.write( "Ask the question:  Can you multiply your way out of the set of integers?\r\n" );
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document.write( "Let's see:  Multiply integer 2 time integer 3.  You get 6 which is also\r\n" );
document.write( "an integer.  So you didn't multiply your way out of the set of integers.\r\n" );
document.write( "How about a negative integer like -7, multiply that by 8.  You get -56\r\n" );
document.write( "which is also an integer.  So you didn't multiply your way out of the set\r\n" );
document.write( "of integers.  So it looks as though you cannot multiply your way out of\r\n" );
document.write( "the set of integers, because if you multiply two integers you always get\r\n" );
document.write( "another integer.  So the answer is: the set of integers is CLOSED for\r\n" );
document.write( "multiplication.  \r\n" );
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document.write( "b. the set of positive integers for subtraction.\r\n" );
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document.write( "Ask the question:  Can you subtract your way out of the set of positive\r\n" );
document.write( "integers?\r\n" );
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document.write( "Let's see:  Subtract positive integer 3 from positive integer 2.  You get -1,\r\n" );
document.write( "which is NOT a positive integer.  So you subtracted your way out of the set of\r\n" );
document.write( "positive integers into the set of negative integers.  So the answer is:\r\n" );
document.write( "the set of positive integers is NOT CLOSED for subtraction.  \r\n" );
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document.write( "c. the set of negative integers for addition.\r\n" );
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document.write( "Ask the question:  Can you add your way out of the set of negative integers?\r\n" );
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document.write( "Let's see:  Add negative integer -2 and negative integer -3.  You get -5 which\r\n" );
document.write( "is also a negative integer.  So you didn't add your way out of the set of\r\n" );
document.write( "negative integers.  In fact you can't add your way out of negative integers, so\r\n" );
document.write( "the answer is: the set of negative integers is CLOSED for addition.\r\n" );
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document.write( "Edwin
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