To solve the problem of finding the value of [tex]\( n(A \cup B) \)[/tex] given that [tex]\( A \subseteq B \)[/tex], [tex]\( n(A) = 50 \)[/tex], and [tex]\( n(B) = 60 \)[/tex], follow these steps:
1. Understand the Union of Sets:
The union of two sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex], denoted as [tex]\( A \cup B \)[/tex], includes all elements that are in [tex]\( A \)[/tex], [tex]\( B \)[/tex], or in both.
2. Given A is a Subset of B:
Since [tex]\( A \subseteq B \)[/tex], all elements of [tex]\( A \)[/tex] are already included in [tex]\( B \)[/tex]. This means that the union of [tex]\( A \)[/tex] and [tex]\( B \)[/tex] does not add any new elements to [tex]\( B \)[/tex]. Therefore, [tex]\( A \cup B \)[/tex] is essentially just [tex]\( B \)[/tex].
3. Applying the Given Information:
Given [tex]\( n(A) = 50 \)[/tex] and [tex]\( n(B) = 60 \)[/tex], we can directly use the fact that all elements of [tex]\( A \)[/tex] are within [tex]\( B \)[/tex].
4. Conclusion:
Because [tex]\( A \subseteq B \)[/tex], the number of elements in [tex]\( A \cup B \)[/tex] is equal to the number of elements in [tex]\( B \)[/tex].
Therefore, the value of [tex]\( n(A \cup B) \)[/tex] is:
[tex]\[
n(A \cup B) = n(B) = 60
\][/tex]
