If A = {1,2,3,4,5} and B = {2,4}, what is (A \ B) ∪ B?
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Answer and explanation
Correct answer: {1,2,3,4,5}
Because B = {2,4} is a subset of A, removing B from A leaves A \ B = {1,3,5}. Taking the union of this remainder with B restores the removed elements: {1,3,5} ∪ {2,4} = {1,2,3,4,5} = A. Therefore option A is correct. This illustrates that (A \ B) ∪ B = A when B is a subset of A.
Frequently asked questions
What is the correct answer to this question?
{1,2,3,4,5}
Why is this the correct answer?
Because B = {2,4} is a subset of A, removing B from A leaves A \ B = {1,3,5}. Taking the union of this remainder with B restores the removed elements: {1,3,5} ∪ {2,4} = {1,2,3,4,5} = A. Therefore option A is correct. This illustrates that (A \ B) ∪ B = A when B is a subset of 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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