If A = {2, 4, 6, 8, 10}, B = {1, 2, 3, 4, 5}, and C = {4, 5, 6, 7}, what is A ∩ (B ∪ C)?
Answer and explanation
Correct answer: {2, 4, 6}
Apply the operations in the indicated order. First form the union B ∪ C, which contains every element appearing in either set: B ∪ C = {1, 2, 3, 4, 5, 6, 7}. Next find the intersection with A. The elements common to A = {2, 4, 6, 8, 10} and this union are 2, 4, and 6. Therefore, A ∩ (B ∪ C) = {2, 4, 6}. Option B misses the common element 2, option C is only the union, and option D contains elements not in the union.
Frequently asked questions
What is the correct answer to this question?
{2, 4, 6}
Why is this the correct answer?
Apply the operations in the indicated order. First form the union B ∪ C, which contains every element appearing in either set: B ∪ C = {1, 2, 3, 4, 5, 6, 7}. Next find the intersection with A. The elements common to A = {2, 4, 6, 8, 10} and this union are 2, 4, and 6. Therefore, A ∩ (B ∪ C) = {2, 4, 6}. Option B misses the common element 2, option C is only the union, and option D contains elements not in the union.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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