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Let [tex][tex]$A=\{7,8,10,11,15,16,17,18,19\}$[/tex][/tex] and [tex][tex]$B=\{1,2,3,5,15,16,20\}$[/tex][/tex].

Find the following:

List the elements in the set [tex][tex]$A \cup B$[/tex][/tex]:

[tex][tex]$A \cup B = \{\square\}$[/tex][/tex]

Enter the elements as a list, separated by commas. If the result is the empty set, enter DN.

Sagot :

GinnyAnsweridn
To find the union of two sets, denoted [tex]\( A \cup B \)[/tex], we compile all the unique elements that are in either set [tex]\( A \)[/tex] or set [tex]\( B \)[/tex].

Given the sets:
[tex]\[ A = \{7, 8, 10, 11, 15, 16, 17, 18, 19\} \][/tex]
[tex]\[ B = \{1, 2, 3, 5, 15, 16, 20\} \][/tex]

We need to list all the unique elements from both sets:

1. Start by listing all the elements of set [tex]\( A \)[/tex]:
[tex]\[ 7, 8, 10, 11, 15, 16, 17, 18, 19 \][/tex]

2. Now list all the elements of set [tex]\( B \)[/tex]:
[tex]\[ 1, 2, 3, 5, 15, 16, 20 \][/tex]

3. Combine these two lists:
[tex]\[ 7, 8, 10, 11, 15, 16, 17, 18, 19, 1, 2, 3, 5, 15, 16, 20 \][/tex]

4. Remove the duplicates (elements that appear in both sets):
[tex]\[ 1, 2, 3, 5, 7, 8, 10, 11, 15, 16, 17, 18, 19, 20 \][/tex]

The unique elements in [tex]\( A \cup B \)[/tex] are:
[tex]\[ A \cup B = \{1, 2, 3, 5, 7, 8, 10, 11, 15, 16, 17, 18, 19, 20\} \][/tex]

So the final answer is:
[tex]\[ A \cup B = \{1, 2, 3, 5, 7, 8, 10, 11, 15, 16, 17, 18, 19, 20\} \][/tex]
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