If A = {2, 4, 6, 8} and B = {1, 2, 3, 4, 5}, how many elements are in A ∪ B?
Answer and explanation
Correct answer: 7
The union contains every distinct element from both sets, with common elements counted only once. Here A ∩ B = {2, 4}, so there are two repeated elements. Using the formula n(A ∪ B) = n(A) + n(B) − n(A ∩ B), we get 4 + 5 − 2 = 7. Indeed, A ∪ B = {1, 2, 3, 4, 5, 6, 8}, which has seven elements. Option C is correct.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
The union contains every distinct element from both sets, with common elements counted only once. Here A ∩ B = {2, 4}, so there are two repeated elements. Using the formula n(A ∪ B) = n(A) + n(B) − n(A ∩ B), we get 4 + 5 − 2 = 7. Indeed, A ∪ B = {1, 2, 3, 4, 5, 6, 8}, which has seven elements. Option C is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
