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If [tex]\( A = \{2, 10, 18, 25\} \)[/tex] and [tex]\( B = \{6, 13, 22, 2, 32, 25\} \)[/tex], then find [tex]\( A \cup B \)[/tex].

a. [tex]\( \{2, 6, 10, 13, 18, 22, 25\} \)[/tex]
b. [tex]\( \{2, 25\} \)[/tex]
c. [tex]\( \{2, 6, 10, 13, 18, 22, 25, 32\} \)[/tex]
d. [tex]\( \{2, 6, 10, 18, 22, 25, 32\} \)[/tex]
e. [tex]\( \{2, 6, 13, 18, 22, 32\} \)[/tex]



Answer :

GinnyAnswer
To find the union of the sets [tex]\(A\)[/tex] and [tex]\(B\)[/tex], we combine all the elements from both sets without any repetition. Here are the steps to determine [tex]\(A \cup B\)[/tex]:

1. List all elements in set [tex]\(A\)[/tex]: [tex]\(\{2, 10, 18, 25\}\)[/tex].
2. List all elements in set [tex]\(B\)[/tex]: [tex]\(\{6, 13, 22, 2, 32, 25\}\)[/tex].

Next, we combine these elements, ensuring that each element appears only once in the resulting set:

3. Start with all elements in [tex]\(A\)[/tex]:
[tex]\(\{2, 10, 18, 25\}\)[/tex].

4. Add elements from [tex]\(B\)[/tex] that are not already in [tex]\(A\)[/tex]:
- [tex]\(6\)[/tex] is not in [tex]\(A\)[/tex], so add [tex]\(6\)[/tex].
- [tex]\(13\)[/tex] is not in [tex]\(A\)[/tex], so add [tex]\(13\)[/tex].
- [tex]\(22\)[/tex] is not in [tex]\(A\)[/tex], so add [tex]\(22\)[/tex].
- [tex]\(2\)[/tex] is already in [tex]\(A\)[/tex], so do not add [tex]\(2\)[/tex].
- [tex]\(32\)[/tex] is not in [tex]\(A\)[/tex], so add [tex]\(32\)[/tex].
- [tex]\(25\)[/tex] is already in [tex]\(A\)[/tex], so do not add [tex]\(25\)[/tex].

Combining all unique elements gives us: [tex]\(\{2, 6, 10, 13, 18, 22, 25, 32\}\)[/tex].

Therefore, the union of sets [tex]\(A\)[/tex] and [tex]\(B\)[/tex] is [tex]\(\{2, 6, 10, 13, 18, 22, 25, 32\}\)[/tex].

Thus, the correct answer is:

c. [tex]\(\{2, 6, 10, 13, 18, 22, 25, 32\}\)[/tex]

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