Question

If A={1,3,7,8,9}, B={2,5,8,11}, and C={1,3,5,7,9}, then what is (A∪C)∩B?

Answer 1

Given:

A = {1, 3, 7, 8, 9}, B = {2, 5, 8, 11}, C = {1, 3, 5, 7, 9}

Required: (A∪C)∩B

Step-by-step explanation:

First, find A∪C.

A∪C is the set of all elements in A or B.

`\text{ A}\cup C=\lbrace1,3,5,7,8,9\rbrace`

Now, take the intersection of A∪C with the set B.

The intersection of two sets A and B is the set of elements common in both sets A and B.

The elements common in A∪C and B are 5 and 8.

`(A\cup C)\cap B=\lbrace5,8\rbrace`

Final Answer: (A∪C)∩B = {5, 8}