The subsets of a set are all possible sets within a set which are:
{1}, {3}, {5}, {7}, {9}, {1,3}, {1,5}, {1,7}, {1,9}, {3,5}, {3,7}, {3,9}, {5,7}, {5,9}, {7,9}, {1,3,5}, {1,3,7}, {1,3,9}, {1,5,7}, {1,5,9}, {1,7,9}, {3,5,7}, {3,5,9}, {3,7,9}, {5,7,9}, {1,3,5,7}, {1,3,5,9}, {1,3,7,9}, {1,5,7,9}, {3,5,7,9}, {1,3,5,7,9}, { }
Notice the pattern:
If we have 0 terms then we have 1 set; { }
1 term ; {a} , { } - 2
2 terms: {a,b}, {a}, {b} , { } - 4
3 terms: {a,b,c}, {a,b}, {a,c}, {b,c}, {a}, {b}, {c}, { } - 8
4 terms: {a,b,c,d}, {a,b,c}, {a,b,d}, {b,c,d}, {a,b}, {a,c}, {a,d}, {b,c}, {b,d}, {c,d}, {a}, {b}, {c}, {d}, { } - 16
Notice that the number of terms is: [tex]2^n[/tex]
