document.write( "Question 968062: How many subsets does the set {w,x,y,z} have? \n" ); document.write( "
Algebra.Com's Answer #591663 by Edwin McCravy(20055)![]() ![]() You can put this solution on YOUR website! \r\n" ); document.write( "It has 4 elements.\r\n" ); document.write( "\r\n" ); document.write( "When making a subset, there are:\r\n" ); document.write( "\r\n" ); document.write( "2 choices to make concerning the element w, (1) to include w or \r\n" ); document.write( "(2) not to include w.\r\n" ); document.write( "\r\n" ); document.write( "For each of those 2 choices to make concerning the element w, there are\r\n" ); document.write( "2 choices to make concerning the element x, (1) to include x or \r\n" ); document.write( "(2) not to include x. That's 2x2 or 4 choices to make concerning w and x.\r\n" ); document.write( "\r\n" ); document.write( "For each of those 4 choices to make concerning the elements w and x, there are\r\n" ); document.write( "2 choices to make concerning the element y, (1) to include y or \r\n" ); document.write( "(2) not to include y. That's 2x2x2 or 8 choices to make concerning w, x, and y.\r\n" ); document.write( "\r\n" ); document.write( "For each of those 8 choices to make concerning the elements w, x, and x, there\r\n" ); document.write( "are 2 choices to make concerning the element z, (1) to include z or \r\n" ); document.write( "(2) not to include z. That's 2x2x2x2 or 16 choices to make concerning w, x, y,\r\n" ); document.write( "and z.\r\n" ); document.write( "\r\n" ); document.write( "so the set {w,x,y,z} has 24 = 16 subsets, including the empty set and\r\n" ); document.write( "the whole set.\r\n" ); document.write( "\r\n" ); document.write( "They are:\r\n" ); document.write( "\r\n" ); document.write( " 1. { }\r\n" ); document.write( " 2. {w}\r\n" ); document.write( " 3. {x}\r\n" ); document.write( " 4. {y}\r\n" ); document.write( " 5. {z}\r\n" ); document.write( " 6. {w,x}\r\n" ); document.write( " 7. {w,y}\r\n" ); document.write( " 8. {w,z}\r\n" ); document.write( " 9. (x,y}\r\n" ); document.write( "10. {x,z}\r\n" ); document.write( "11. {y,z}\r\n" ); document.write( "12. {w,x,y}\r\n" ); document.write( "13. (w,x,z}\r\n" ); document.write( "14. {w,y,z}\r\n" ); document.write( "15. (x,y,z}\r\n" ); document.write( "16. {w,x,y,z}\r\n" ); document.write( "\r\n" ); document.write( "Edwin\n" ); document.write( " |