If A ⊆ B, n(A) = 18, and n(B) = 45, what is n(B − A)?
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Answer and explanation
Correct answer: 27
Since A is a subset of B, every element of A is already included in B. The set B − A contains the elements that belong to B but not to A. Therefore, its cardinality is n(B − A) = n(B) − n(A) = 45 − 18 = 27. In a Venn diagram, A lies inside B, and the region of B outside A contains these 27 elements.
Frequently asked questions
What is the correct answer to this question?
27
Why is this the correct answer?
Since A is a subset of B, every element of A is already included in B. The set B − A contains the elements that belong to B but not to A. Therefore, its cardinality is n(B − A) = n(B) − n(A) = 45 − 18 = 27. In a Venn diagram, A lies inside B, and the region of B outside A contains these 27 elements.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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