If A = {2, 3, 5, 7} and B = {5, 7, 11, 13}, how many elements are in A ∪ B?
Answer and explanation
Correct answer: 6
The union contains every distinct element appearing in either set. Combining A and B gives A ∪ B = {2, 3, 5, 7, 11, 13}, which has six elements. The same result follows from n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 4 + 4 − 2 = 6, because 5 and 7 are common and must not be counted twice. Hence, option B is correct.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
The union contains every distinct element appearing in either set. Combining A and B gives A ∪ B = {2, 3, 5, 7, 11, 13}, which has six elements. The same result follows from n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 4 + 4 − 2 = 6, because 5 and 7 are common and must not be counted twice. Hence, option B 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).
