Let $U=\{1,2,3,4,5,6,7,8\}, A=\{1,2,3,4\}$, and $B=\{2,5,6\}$. Find the set $A \cap B$.
$A \cap B=\square$
(Use a comma to separate answers as needed.)
Answer (1)
Identify the elements of set A and set B.
Find the elements that are common to both sets.
The intersection of A and B is the set containing the common elements: A ∩ B = { 2 } .
The final answer is 2 .
Explanation
Understanding the Problem We are given two sets, A = { 1 , 2 , 3 , 4 } and B = { 2 , 5 , 6 } . We need to find the intersection of these two sets, which means we need to identify the elements that are present in both set A and set B.
Finding Common Elements Looking at the elements of set A and set B, we can see that the number 2 is the only element that appears in both sets. Therefore, the intersection of A and B is the set containing only the element 2.
Final Answer Thus, A ∩ B = { 2 } .
Examples
Understanding set intersections is crucial in database management. Imagine you have two lists of customers: one list (A) contains customers who bought product X, and another list (B) contains customers who live in a specific city. The intersection A ∩ B would give you a list of customers who bought product X and live in that specific city. This is useful for targeted marketing campaigns or analyzing customer behavior within specific regions.
