To determine [tex]\( B \cap A \)[/tex] (the intersection of sets [tex]\(B\)[/tex] and [tex]\(A\)[/tex]), we must identify all elements that are common to both sets [tex]\(A\)[/tex] and [tex]\(B\)[/tex].
Let's start by listing the elements of each set:
- Set [tex]\(A\)[/tex] is [tex]\(\{2, 4, 6, 8, 10, 12\}\)[/tex].
- Set [tex]\(B\)[/tex] is [tex]\(\{3, 6, 9, 12, 15\}\)[/tex].
Now, we will compare these elements to find the common ones.
- The element [tex]\(2\)[/tex] is in [tex]\(A\)[/tex] but not in [tex]\(B\)[/tex].
- The element [tex]\(4\)[/tex] is in [tex]\(A\)[/tex] but not in [tex]\(B\)[/tex].
- The element [tex]\(6\)[/tex] is in both [tex]\(A\)[/tex] and [tex]\(B\)[/tex].
- The element [tex]\(8\)[/tex] is in [tex]\(A\)[/tex] but not in [tex]\(B\)[/tex].
- The element [tex]\(10\)[/tex] is in [tex]\(A\)[/tex] but not in [tex]\(B\)[/tex].
- The element [tex]\(12\)[/tex] is in both [tex]\(A\)[/tex] and [tex]\(B\)[/tex].
The elements that are common to both sets [tex]\(A\)[/tex] and [tex]\(B\)[/tex] are [tex]\(6\)[/tex] and [tex]\(12\)[/tex].
Therefore, the intersection [tex]\( B \cap A \)[/tex] is:
[tex]\[ B \cap A = \{12, 6\} \][/tex]
