document.write( "Question 590302: Let U = {q, r, s, t, u, v, w, x, y, z}
\n" ); document.write( " A = {q, s, u, w, y}
\n" ); document.write( " B = {q, s, y, z}
\n" ); document.write( " C = {v, w, x, y, z}. \r
\n" ); document.write( "\n" ); document.write( "Determine the following.
\n" ); document.write( "A ∪ (B ∩ C) \n" ); document.write( "
Algebra.Com's Answer #375099 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"∪\" = UNIOM\r\n" );
document.write( "∪ means to form the set consisting of every element that is either a member\r\n" );
document.write( "of the set on the left of ∪ or a member of the set on the right of ∪.\r\n" );
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document.write( "\"∩\" = INTERSECTION\r\n" );
document.write( "∩ means to form the set consisting of ONLY those elements that are in common\r\n" );
document.write( "to both the set on the left of ∩ and to the set on the right of ∩. \r\n" );
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document.write( " Substitute the sets for the letters: \r\n" );
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document.write( "                      A        ∪ (      B       ∩        C        )\r\n" );
document.write( "               {q, s, u, w, y} ∪ ( {q, s, y, z} ∩ {v, w, x, y, z} )\r\n" );
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document.write( "First we work inside the parentheses, it has ∩, so we form the\r\n" );
document.write( "set consisting of ONLY those elements that are incommon to both sets\r\n" );
document.write( "{q, s, y, z} and {v, w, x, y, z}.  We see that y and z are the only\r\n" );
document.write( "ones that are in common to both sets, so the set to form is {y, z}.\r\n" );
document.write( "So far we have:\r\n" );
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document.write( "                      A        ∪ (      B       ∩        C        )\r\n" );
document.write( "               {q, s, u, w, y} ∪ ( {q, s, y, z} ∩ {v, w, x, y, z} )\r\n" );
document.write( "               {q, s, u, w, y} ∪              {y, z}              \r\n" );
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document.write( "Now we have only a ∪, and so we form the set that consists of all the\r\n" );
document.write( "elements in {q, s, u, w, y} together withe both elements of {y, z}. So\r\n" );
document.write( "we end up with this:\r\n" );
document.write( "                      A        ∪ (      B       ∩        C        )\r\n" );
document.write( "               {q, s, u, w, y} ∪ ( {q, s, y, z} ∩ {v, w, x, y, z} )\r\n" );
document.write( "               {q, s, u, w, y} ∪              {y, z}\r\n" );
document.write( "                                {q, s, u, w, y, z}\r\n" );
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document.write( "[Notice that we only need to list the y one time even though it is a\r\n" );
document.write( "member of both sets.]\r\n" );
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document.write( "Edwin

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