If A = {x : x ∈ ℕ, x ≤ 12}, B = {x ∈ A : x is even}, and C = {x ∈ A : x is prime}, how many elements are in B ∪ C?
Answer and explanation
Correct answer: 9
Assuming ℕ includes the positive natural numbers, A = {1, 2, 3, ..., 12}. The even elements are B = {2, 4, 6, 8, 10, 12}, and the prime elements are C = {2, 3, 5, 7, 11}. The union contains every element appearing in either set: B ∪ C = {2, 3, 4, 5, 6, 7, 8, 10, 11, 12}. The common element 2 is counted only once, so the union has 9 elements. Equivalently, |B ∪ C| = |B| + |C| − |B ∩ C| = 6 + 5 − 1 = 10? Careful: the displayed union omits no elements; it contains 10 elements, so the correct answer is B.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
Assuming ℕ includes the positive natural numbers, A = {1, 2, 3, ..., 12}. The even elements are B = {2, 4, 6, 8, 10, 12}, and the prime elements are C = {2, 3, 5, 7, 11}. The union contains every element appearing in either set: B ∪ C = {2, 3, 4, 5, 6, 7, 8, 10, 11, 12}. The common element 2 is counted only once, so the union has 9 elements. Equivalently, |B ∪ C| = |B| + |C| − |B ∩ C| = 6 + 5 − 1 = 10? Careful: the displayed union omits no elements; it contains 10 elements, so the correct answer is B.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
