Answer to Question #310359 in Discrete Mathematics for rishi lakhera

Question

If U = {1, 3, 5, 7, 9, 11, 13}, then which of the following are subsets of U.

Answer 1

Solution

The given set is $U = \{1, 3, 5, 7, 9, 11, 13\}$

There are 7 elements of the given set. Therefore there will be $2^7=128$ subsets of the given set. These are

Empty Set

{},

Subsets with one element

{1}, {3}, {5}, {7}, {9}, {11}, {13}, one element subsets

Subsets with two elements

{1, 3}, {1, 5}, {3, 5}, {1, 7}, {3, 7}, {5, 7}, {1, 9}, {3, 9}, {5, 9}, {7, 9}, {1, 11}, {3, 11}, {5, 11}, {7, 11}, {9, 11}, {1, 13}, {3, 13}, {5, 13}, {7, 13}, {9, 13}, {11, 13},

Subsets with three elements

{1, 3, 5}, {1, 3, 7}, {1, 5, 7}, {3, 5, 7}, {1, 3, 9}, {1, 5, 9}, {3, 5, 9}, {1, 7, 9}, {3, 7, 9}, {5, 7, 9}, {1, 3, 11}, {1, 5, 11}, {3, 5, 11}, {1, 7, 11}, {3, 7, 11}, {5, 7, 11}, {1, 9, 11}, {3, 9, 11}, {5, 9, 11}, {7, 9, 11}, {1, 3, 13}, {1, 5, 13}, {3, 5, 13}, {1, 7, 13}, {3, 7, 13}, {5, 7, 13}, {1, 9, 13}, {3, 9, 13}, {5, 9, 13}, {7, 9, 13}, {1, 11, 13}, {3, 11, 13}, {5, 11, 13}, {7, 11, 13}, {9, 11, 13},

Subsets with four elements

{1, 3, 5, 7}, {1, 3, 5, 9}, {1, 3, 7, 9}, {1, 5, 7, 9}, {3, 5, 7, 9}, {1, 3, 5, 11}, {1, 3, 7, 11}, {1, 5, 7, 11}, {3, 5, 7, 11}, {1, 3, 9, 11}, {1, 5, 9, 11}, {3, 5, 9, 11}, {1, 7, 9, 11}, {3, 7, 9, 11}, {5, 7, 9, 11}, {1, 3, 5, 13}, {1, 3, 7, 13}, {1, 5, 7, 13}, {3, 5, 7, 13}, {1, 3, 9, 13}, {1, 5, 9, 13}, {3, 5, 9, 13}, {1, 7, 9, 13}, {3, 7, 9, 13}, {5, 7, 9, 13}, {1, 3, 11, 13}, {1, 5, 11, 13}, {3, 5, 11, 13}, {1, 7, 11, 13}, {3, 7, 11, 13}, {5, 7, 11, 13}, {1, 9, 11, 13}, {3, 9, 11, 13}, {5, 9, 11, 13}, {7, 9, 11, 13},

Subsets with six elements

{1, 3, 5, 7, 9}, {1, 3, 5, 7, 11}, {1, 3, 5, 9, 11}, {1, 3, 7, 9, 11}, {1, 5, 7, 9, 11}, {3, 5, 7, 9, 11}, {1, 3, 5, 7, 13}, {1, 3, 5, 9, 13}, {1, 3, 7, 9, 13}, {1, 5, 7, 9, 13}, {3, 5, 7, 9, 13}, {1, 3, 5, 11, 13}, {1, 3, 7, 11, 13}, {1, 5, 7, 11, 13}, {3, 5, 7, 11, 13}, {1, 3, 9, 11, 13}, {1, 5, 9, 11, 13}, {3, 5, 9, 11, 13}, {1, 7, 9, 11, 13}, {3, 7, 9, 11, 13}, {5, 7, 9, 11, 13},

{1, 3, 5, 7, 9, 11}, {1, 3, 5, 7, 9, 13}, {1, 3, 5, 7, 11, 13}, {1, 3, 5, 9, 11, 13}, {1, 3, 7, 9, 11, 13}, {1, 5, 7, 9, 11, 13}, {3, 5, 7, 9, 11, 13},

Subset with seven elements

{1, 3, 5, 7, 9, 11, 13}