document.write( "Question 1126619: If A = {all prime numbers between 1 and 100}, B = {2,4,6,...,98,100}, and C = {3,6,9,...,96,99}, how many elements does (A union B) intersection C have? \n" ); document.write( "

Algebra.Com's Answer #742976 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "From the elementary set theory,  {(A U B) n C}}} = {(A n C) U (B n C)}.\r\n" );
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document.write( "    {(A n C)} is the set of all prime numbers between 1 and 100 intersected with the set of all integer numbers multiple 3 in this domain.\r\n" );
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document.write( "    So, {{A n C)} consists of one single element {3}.\r\n" );
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document.write( "    {(B n C)} is the set of all even numbers between 1 and 100 intersected with the set of all integer numbers multiple of 3 in this domain.\r\n" );
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document.write( "    So, {(B n C)} is the set of all multiple of 6 between 1 and 100 inclusively.\r\n" );
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document.write( "Therefore,  \r\n" );
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document.write( "    {(A U B) n C}}} = {(A n C) U (B n C)} = the set of all multiple of 6 between 1 and 100 inclusively  PLUS  the number 3.\r\n" );
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document.write( "    The amount of all integers multiple of 6 between 1 and 100 inclusively is  16   (because   = 16.66. . . ).\r\n" );
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document.write( "    Plus that single \"3\" gives you the answer of 17.\r\n" );
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\n" ); document.write( "\n" ); document.write( "The tutor @MathLover1 missed the number \"54\" in her final list.\r
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