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.
We start with set [tex]\( A \)[/tex]:
[tex]\[ A = \{2, 4, 6, 8, 10, 12\} \][/tex]
Next, we look at set [tex]\( B \)[/tex]:
[tex]\[ B = \{3, 6, 9, 12, 15\} \][/tex]
Now, we check each element of set [tex]\( A \)[/tex] to see if it is also in set [tex]\( B \)[/tex].
1. The element 2 is in [tex]\( A \)[/tex], but not in [tex]\( B \)[/tex].
2. The element 4 is in [tex]\( A \)[/tex], but not in [tex]\( B \)[/tex].
3. The element 6 is in [tex]\( A \)[/tex] and also in [tex]\( B \)[/tex].
4. The element 8 is in [tex]\( A \)[/tex], but not in [tex]\( B \)[/tex].
5. The element 10 is in [tex]\( A \)[/tex], but not in [tex]\( B \)[/tex].
6. The element 12 is in [tex]\( A \)[/tex] and also in [tex]\( B \)[/tex].
From this, we see that the common elements are 6 and 12.
Therefore, the intersection of sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex] is:
[tex]\[ A \cap B = \{12, 6\} \][/tex]
So, the result of the intersection [tex]\( A \cap B \)[/tex] is:
[tex]\[ \boxed{[12, 6]} \][/tex]
