If A = {2, 4, 6, 8, 10} and B = {1, 2, 3, 4, 5}, how many elements are in A ∪ B?
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Answer and explanation
Correct answer: 8
The union contains all distinct elements from both sets. Combining A and B gives A ∪ B = {1, 2, 3, 4, 5, 6, 8, 10}. The elements 2 and 4 occur in both sets, but each is counted only once in a set union. Consequently, the union has 8 elements. Equivalently, |A ∪ B| = |A| + |B| − |A ∩ B| = 5 + 5 − 2 = 8.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The union contains all distinct elements from both sets. Combining A and B gives A ∪ B = {1, 2, 3, 4, 5, 6, 8, 10}. The elements 2 and 4 occur in both sets, but each is counted only once in a set union. Consequently, the union has 8 elements. Equivalently, |A ∪ B| = |A| + |B| − |A ∩ B| = 5 + 5 − 2 = 8.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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