Operations on Sets

Set operations like union and intersection help us combine or compare sets. The union of two sets includes all elements that belong to either set or both. The intersection includes only the elements that belong to both sets. Let’s see how these operations work with an example.

Imagine a coach evaluating students trying out for a track and field team. The list of all students at the tryout makes up the universal set.

After testing the students, the coach creates two subsets based on their skills: Set A lists students who can run fast, and Set B lists students who can jump high.

First, the coach may want a shortlist of students with at least one skill needed for the team. To do this, the coach takes the union of the two sets. Here, the union of A and B lists students who can run fast, jump high, or do both.

Next, the coach may want students with both skills. To do this, the coach finds the intersection, which includes only the students who appear in both sets. Here, the intersection of A and B lists students who can both run fast and jump high, making them good choices for hurdling.

In this way, set operations help us combine and compare sets to make decisions from organized information.