If A △ B = (A − B) ∪ (B − A), where A = {a, b, c, d} and B = {b, d, e, f}, find A △ B.
Answer and explanation
Correct answer: {a, c, e, f}
The symmetric difference contains elements that occur in exactly one of the two sets. From A, the elements not in B are A − B = {a, c}. From B, the elements not in A are B − A = {e, f}. Their union is therefore A △ B = {a, c, e, f}. The common elements b and d are excluded because they belong to both sets.
Frequently asked questions
What is the correct answer to this question?
{a, c, e, f}
Why is this the correct answer?
The symmetric difference contains elements that occur in exactly one of the two sets. From A, the elements not in B are A − B = {a, c}. From B, the elements not in A are B − A = {e, f}. Their union is therefore A △ B = {a, c, e, f}. The common elements b and d are excluded because they belong to both sets.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
