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 [tex]\( A \)[/tex] and [tex]\( B \)[/tex].
Given:
[tex]\[ A = \{2, 4, 6, 8, 10, 12\} \][/tex]
[tex]\[ B = \{3, 6, 9, 12, 15\} \][/tex]
We'll go through each element of set [tex]\( A \)[/tex] and check whether it also belongs to set [tex]\( B \)[/tex].
1. The element [tex]\( 2 \)[/tex] is in [tex]\( A \)[/tex] but not in [tex]\( B \)[/tex].
2. The element [tex]\( 4 \)[/tex] is in [tex]\( A \)[/tex] but not in [tex]\( B \)[/tex].
3. The element [tex]\( 6 \)[/tex] is in [tex]\( A \)[/tex] and also in [tex]\( B \)[/tex].
4. The element [tex]\( 8 \)[/tex] is in [tex]\( A \)[/tex] but not in [tex]\( B \)[/tex].
5. The element [tex]\( 10 \)[/tex] is in [tex]\( A \)[/tex] but not in [tex]\( B \)[/tex].
6. The element [tex]\( 12 \)[/tex] is in [tex]\( A \)[/tex] and also in [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 of sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex] is:
[tex]\[ A \cap B = \{6, 12\} \][/tex]
