If A ⊆ B, n(B) = 83, n(A) = 47, and n(U) = 120, what is n(B − A)?
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Answer and explanation
Correct answer: 36
Because A is a subset of B, every element of A lies inside B. The set B − A therefore consists of the elements belonging to B but not to A. Its cardinality is n(B − A) = n(B) − n(A) = 83 − 47 = 36. The universal-set size is not needed for this difference, so option A is the only correct answer.
Frequently asked questions
What is the correct answer to this question?
36
Why is this the correct answer?
Because A is a subset of B, every element of A lies inside B. The set B − A therefore consists of the elements belonging to B but not to A. Its cardinality is n(B − A) = n(B) − n(A) = 83 − 47 = 36. The universal-set size is not needed for this difference, so option A is the only correct answer.
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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