What is the difference between union and intersection in set theory?

Can you explain the difference between union and intersection in set theory?

Sure! In set theory, the union of two sets includes all elements from both sets, while the intersection includes only the elements that are common to both sets.

Can you give me an example of each?

Of course! If Set A = {1, 2, 3} and Set B = {2, 3, 4}, then the union (A ∪ B) is {1, 2, 3, 4}, and the intersection (A ∩ B) is {2, 3}.

What if one set is empty?

If one set is empty, the union will be the other set, but the intersection will be empty. For example, if Set A = {1, 2} and Set B = {}, then A ∪ B = {1, 2} and A ∩ B = {}.

Are there any real-world applications for these concepts?

Yes! Union and intersection are used in databases for querying data, in probability for events, and in various fields like computer science and statistics.