If A = {1, 4, 9, 16, 25} and B = {2, 4, 8, 16, 32}, what is (A − B) ∪ (B − A)?
Answer and explanation
Correct answer: {1, 2, 8, 9, 25, 32}
A − B contains elements present in A but absent from B, so A − B = {1, 9, 25}. Similarly, B − A = {2, 8, 32}. Taking their union gives {1, 9, 25} ∪ {2, 8, 32} = {1, 2, 8, 9, 25, 32}. This operation is also called the symmetric difference because common elements 4 and 16 are excluded. Thus option B is correct.
Frequently asked questions
What is the correct answer to this question?
{1, 2, 8, 9, 25, 32}
Why is this the correct answer?
A − B contains elements present in A but absent from B, so A − B = {1, 9, 25}. Similarly, B − A = {2, 8, 32}. Taking their union gives {1, 9, 25} ∪ {2, 8, 32} = {1, 2, 8, 9, 25, 32}. This operation is also called the symmetric difference because common elements 4 and 16 are excluded. Thus option B 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).
