Question 2 Practice similar questions Score: 1 of 1 point If \( A \) and \( B \) are two sets such that \( n(A \cup B)=100, n(A)=32 \), and \( n(B)=72 \). How many elements does \( A \cap B \) have? 4 Prevt Submit answer Attempts: 1/10 That's correct! You've applied the concept of Terminology correctly. Find this question difficult? Do you know you can practice another version of this question?

To find the number of elements in the intersection of sets \( A \) and \( B \) (denoted as \( A \cap B \)), we can use the formula for the union of two sets: \[ n(A \cup B) = n(A) + n(B) - n(A \cap B) \] Plugging in the values gives us: \[ 100 = 32 + 72 - n(A \cap B) \] This simplifies to \( n(A \cap B) = 4 \). Voila! It's interesting to note how these set operations have real-world applications. For example, in database management, understanding how to combine and intersect datasets can optimize queries and improve data retrieval efficiency. Companies use these set principles to analyze customer data and understand overlapping interests between different products or services, proving just how essential this mathematical concept is in practical scenarios.