Questions: Find the set (A cup B) U=1,2,3,4,5,6,7,8,9,10 A=1,5,6,8 B=3,1,9 Select the correct choice below and, if necessary, fill in the answer box to complete your choice A. (A cup B=) (Use a comma to separate answers as needed.) B. (A cup B) is the empty set

Find the set (A cup B)

U=1,2,3,4,5,6,7,8,9,10
A=1,5,6,8
B=3,1,9

Select the correct choice below and, if necessary, fill in the answer box to complete your choice
A. (A cup B=) (Use a comma to separate answers as needed.)
B. (A cup B) is the empty set

Transcript text: Find the set $A \cup B$ \[ \begin{array}{l} U=\{1,2,3,4,5,6,7,8,9,10\} \\ A=\{1,5,6,8\} \\ B=\{3,1,9\} \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice A. $A \cup B=$ $\square$ (Use a comma to separate answers as needed.) B. $A \cup B$ is the empty set

Solution

Solution Steps

To find the union of sets $ A $ and $ B $, we need to combine all the unique elements from both sets. The union of two sets $ A $ and $ B $ is denoted as $ A \cup B $ and includes every element that is in $ A $, in $ B $, or in both.

Step 1: Define the Sets

We are given the universal set $ U $ and two subsets $ A $ and $ B $: \[ U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \] \[ A = \{1, 5, 6, 8\} \] \[ B = \{3, 1, 9\} \]

Step 2: Find the Union of Sets $ A $ and $ B $

The union of two sets $ A $ and $ B $, denoted as $ A \cup B $, includes all unique elements that are in $ A $, in $ B $, or in both.

Step 3: Combine and Sort the Elements

Combining the elements of $ A $ and $ B $: \[ A \cup B = \{1, 5, 6, 8\} \cup \{3, 1, 9\} \] This results in: \[ A \cup B = \{1, 3, 5, 6, 8, 9\} \]