To find the intersection of sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex], we need to identify the elements that are common to both sets. Here are the steps to solve it:
1. List the elements of set [tex]\( A \)[/tex]:
[tex]\[
A = \{2, 4, 6, 8, 10, 12\}
\][/tex]
2. List the elements of set [tex]\( B \)[/tex]:
[tex]\[
B = \{3, 6, 9, 12, 15\}
\][/tex]
3. Identify the common elements between set [tex]\( A \)[/tex] and set [tex]\( B \)[/tex]:
- The elements of [tex]\( A \)[/tex] are: 2, 4, 6, 8, 10, 12.
- The elements of [tex]\( B \)[/tex] are: 3, 6, 9, 12, 15.
4. Check each element of [tex]\( A \)[/tex] if it is also in [tex]\( B \)[/tex]:
- 2 is not in [tex]\( B \)[/tex].
- 4 is not in [tex]\( B \)[/tex].
- 6 is in [tex]\( B \)[/tex].
- 8 is not in [tex]\( B \)[/tex].
- 10 is not in [tex]\( B \)[/tex].
- 12 is in [tex]\( B \)[/tex].
5. List the common elements to form the intersection set [tex]\( A \cap B \)[/tex]:
[tex]\[
A \cap B = \{6, 12\}
\][/tex]
Thus, the intersection of sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex] is [tex]\(\{6, 12\}\)[/tex].
