If A △ B = {7} and A ⊆ B, what is B − A equal to?
Answer and explanation
Correct answer: {7}
The symmetric difference is defined by A △ B = (A − B) ∪ (B − A). Since A ⊆ B, no element of A lies outside B, so A − B = ∅. Therefore A △ B = B − A. Given that A △ B = {7}, it follows immediately that B − A = {7}. Hence option A is correct; the empty-set option would contradict the given nonempty symmetric difference.
Frequently asked questions
What is the correct answer to this question?
{7}
Why is this the correct answer?
The symmetric difference is defined by A △ B = (A − B) ∪ (B − A). Since A ⊆ B, no element of A lies outside B, so A − B = ∅. Therefore A △ B = B − A. Given that A △ B = {7}, it follows immediately that B − A = {7}. Hence option A is correct; the empty-set option would contradict the given nonempty symmetric difference.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
