Question

let u be the universal set, where: u = {1,2,3,…,18,19,20} let sets a and b be subsets of u, where: set a = {3,4,11,13,14,15,16,17} set b = {3,4,6,8,13,20} find the following: list the elements in the set ( a cup b ): ( a cup b = { ) enter the elements as a list, separated by commas. if the result is the empty set, enter dne list the elements in the set ( a cap b ): ( a cap b = { ) enter the elements as a list, separated by commas. if the result is the empty set, enter dne you may want to draw a venn diagram to help answer this question.

Explanation:

Step1: Find \( A \cup B \)

The union of two sets \( A \) and \( B \), denoted \( A \cup B \), is the set of all elements that are in \( A \) or in \( B \) (or in both).
Set \( A=\{3,4,11,13,14,15,16,17\} \) and set \( B = \{3,4,6,8,13,20\} \).
Combining all unique elements from \( A \) and \( B \):
Start with elements of \( A \): \( 3,4,11,13,14,15,16,17 \)
Add elements of \( B \) that are not already in \( A \): \( 6,8,20 \)
So \( A \cup B=\{3,4,6,8,11,13,14,15,16,17,20\} \)

Step2: Find \( A \cap B \)

The intersection of two sets \( A \) and \( B \), denoted \( A \cap B \), is the set of all elements that are in both \( A \) and \( B \).
Looking for common elements in \( A=\{3,4,11,13,14,15,16,17\} \) and \( B = \{3,4,6,8,13,20\} \):
Common elements are \( 3,4,13 \)
So \( A \cap B = \{3,4,13\} \)

Answer:

For \( A \cup B \): \( 3,4,6,8,11,13,14,15,16,17,20 \)
For \( A \cap B \): \( 3,4,13 \)