If A = {1, 2, 3, 4, 5}, B = {2, 4, 6, 8}, and C = {1, 4, 7, 8}, find A ∩ (B ∪ C).
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Answer and explanation
Correct answer: {1, 2, 4}
Evaluate the parentheses first. The union B ∪ C contains all distinct elements from B and C: {1, 2, 4, 6, 7, 8}. Now intersect this set with A = {1, 2, 3, 4, 5}. The common elements are 1, 2, and 4; elements 6, 7, and 8 are not in A. Therefore A ∩ (B ∪ C) = {1, 2, 4}, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
{1, 2, 4}
Why is this the correct answer?
Evaluate the parentheses first. The union B ∪ C contains all distinct elements from B and C: {1, 2, 4, 6, 7, 8}. Now intersect this set with A = {1, 2, 3, 4, 5}. The common elements are 1, 2, and 4; elements 6, 7, and 8 are not in A. Therefore A ∩ (B ∪ C) = {1, 2, 4}, so option A 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).
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