To determine the minimum number of elements in the intersection of two sets [tex]\( X \)[/tex] and [tex]\( Y \)[/tex], denoted as [tex]\( n(X \cap Y) \)[/tex], we need to consider the case when the sets are disjoint.
When two sets are disjoint, they have no elements in common. Therefore, the intersection of disjoint sets is an empty set. The number of elements in an empty set is zero.
Given:
- [tex]\( n(X) = 15 \)[/tex]
- [tex]\( n(Y) = 7 \)[/tex]
If [tex]\( X \)[/tex] and [tex]\( Y \)[/tex] are disjoint, then:
[tex]\[ n(X \cap Y) = 0 \][/tex]
Thus, the minimum [tex]\( n(X \cap Y) \)[/tex] is [tex]\( \mathbf{0} \)[/tex].
