Question

Suppose that U (the universal set), A and B are sets, given as shown below. U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10), A = {1, 4, 6, 8, 9, 10), and B = {1,5,9}. Find each of the following sets. Enter your answer by listing the elements in increasing order, separated by commas. Do not put a comma after the last number. If the set is empty, enter DNE. A'UB= {1,2,3,5,7,9 "} A' B' = {2,3,7 } An B' = {4,6,8,10 }

Answer 1

A' U B = {2,3,5,7,8}

A' n B' = {2,3,7}

A n B' = {4,6,8,10}

Explanation:

In our problem, the universal set is:

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

We also have:

A = {1, 4, 6, 8, 9, 10}

B = {1,5,9}.

The complement of a set is a set made by every element that is contained in the universal set and is not contained in the set. So

A' = {2,3,5,7}

B' = {2,3,4,6,7,8,10}

The union of two sets is the set that contains every element that is in at least one of those sets: So

A' U B = {2,3,5,7,8}

The intersection of two sets is the set that contains every element that is in both of those sets. So:

A' n B' = {2,3,7}

A n B' = {4,6,8,10}