Sure, let's solve the problem step by step.
1. Understanding the Question:
The question asks us to find the intersection of two sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex] which are given as:
[tex]\[
A = \{1, 2, 5, 9, 10\}
\][/tex]
[tex]\[
B = \{2, 9, 13, 18, 20\}
\][/tex]
The intersection of two sets, denoted as [tex]\( A \cap B \)[/tex], consists of elements that are common to both sets.
2. Identify Common Elements:
- First element in [tex]\( A \)[/tex] is 1. Is it in [tex]\( B \)[/tex]? No.
- Next element in [tex]\( A \)[/tex] is 2. Is it in [tex]\( B \)[/tex]? Yes.
- Next element in [tex]\( A \)[/tex] is 5. Is it in [tex]\( B \)[/tex]? No.
- Next element in [tex]\( A \)[/tex] is 9. Is it in [tex]\( B \)[/tex]? Yes.
- Last element in [tex]\( A \)[/tex] is 10. Is it in [tex]\( B \)[/tex]? No.
Thus, the numbers that are in both sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are 2 and 9.
3. Write the Intersection:
The intersection [tex]\( A \cap B \)[/tex] is the set of common elements identified:
[tex]\[
A \cap B = \{2, 9\}
\][/tex]
4. Select the Correct Answer from the Given Options:
The correct answer should be [tex]\(\{2, 9\}\)[/tex]. However, none of the provided options exactly match this set. Therefore, the correct intersection set [tex]\( \{2, 9\} \)[/tex] is not listed as an option. Hence, the correct conclusion is:
- There is no correct answer given in the provided options.
So, the final answer is that none of the given options correctly represent the intersection of sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex]. The correct intersection is [tex]\( \{2, 9\} \)[/tex].
