If A ∩ B = {3, 5}, A \ B = {1, 7}, and B \ A = {2, 9}, what is A?
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Answer and explanation
Correct answer: {1, 3, 5, 7}
The set A consists of two disjoint parts: the elements that belong only to A, namely A \ B = {1, 7}, and the elements common to A and B, namely A ∩ B = {3, 5}. Hence A = (A \ B) ∪ (A ∩ B) = {1, 7} ∪ {3, 5} = {1, 3, 5, 7}. The elements 2 and 9 belong only to B, so they must not be included in A.
Frequently asked questions
What is the correct answer to this question?
{1, 3, 5, 7}
Why is this the correct answer?
The set A consists of two disjoint parts: the elements that belong only to A, namely A \ B = {1, 7}, and the elements common to A and B, namely A ∩ B = {3, 5}. Hence A = (A \ B) ∪ (A ∩ B) = {1, 7} ∪ {3, 5} = {1, 3, 5, 7}. The elements 2 and 9 belong only to B, so they must not be included in A.
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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