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\n" ); document.write( "Without writing them down what are the number of subsets of the set A = {a, b, c, d, e, f}? Of set B = {a, b, c, d, e, f, g, h, i, j}?
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document.write( "Take any subset of A, say S. There are 5 elements in A.\r\n" );
document.write( "Therefore there are five questions we can ask about the \r\n" );
document.write( "subset S, relative to each member of A:\r\n" );
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document.write( "1. Does S contain \"a\" as a member? (Yes or No)\r\n" );
document.write( "2. Does S contain \"b\" as a member? (Yes or No)\r\n" );
document.write( "3. Does S contain \"c\" as a member? (Yes or No)\r\n" );
document.write( "4. Does S contain \"d\" as a member? (Yes or No)\r\n" );
document.write( "5. Does S contain \"e\" as a member? (Yes or No)\r\n" );
document.write( "6. Does S contain \"f\" as a member? (Yes or No)\r\n" );
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document.write( "There are 2 ways to answer question 1, so that's 2 ways.\r\n" );
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document.write( "For each of those 2 ways to answer question 1, \r\n" );
document.write( "there are 2 ways to answer question 2, so that's 2^2 ways.\r\n" );
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document.write( "For each of those 2^2 ways to answer questions 1 and 2, \r\n" );
document.write( "there are 2 ways to answer question 3, so that's 2^3 ways.\r\n" );
document.write( "ways. \r\n" );
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document.write( "For each of those 2^3 ways to answer questions 1 thru 3, \r\n" );
document.write( "there are 2 ways to answer question 4, so that's 2^4 ways.\r\n" );
document.write( "ways. \r\n" );
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document.write( "For each of those 2^4 ways to answer questions 1 thru 4, \r\n" );
document.write( "there are 2 ways to answer question 5, so that's 2^5 ways.\r\n" );
document.write( "ways. \r\n" );
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document.write( "For each of those 2^5 ways to answer questions 1 thru 5, \r\n" );
document.write( "there are 2 ways to answer question 6, so that's 2^6 ways.\r\n" );
document.write( "ways.\r\n" );
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document.write( "So that makes 2^6 or 64 subsets, counting the empty or null\r\n" );
document.write( "set as one subset and the entire set as another subset.\r\n" );
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document.write( "When we answer \"no\" to all 6 questions, that is the null set.\r\n" );
document.write( "When we answer \"yes\" to all 6 questions, that is the entire set.\r\n" );
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document.write( "--------------------\r\n" );
document.write( "So in general,\r\n" );
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document.write( "A set that contains n elements or members has exactly 2^n subsets.\r\n" );
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document.write( "Therefore\r\n" );
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document.write( "B = {a, b, c, d, e, f, g, h, i, j}\r\n" );
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document.write( "has 10 members or elements, so B has 2^10 or 1024 subsets.\r\n" );
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document.write( "Edwin \n" );
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