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Class 10MathematicsSetsOperations on Sets (Union, Intersection, Difference)EasyLevel 14

If n(B − A) = 13 and n(A ∩ B) = 6, what is n(B)?

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Answer and explanation

Correct answer: 19

Every element of B belongs either to the part only in B, B − A, or to the common part A ∩ B. These two regions do not overlap, so their cardinalities can be added: n(B) = n(B − A) + n(A ∩ B) = 13 + 6 = 19. Thus option C is correct. Option B omits the six common elements.

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setscardinalityset differenceintersectionVenn diagramsOperations on Sets (UnionDifference)operations on sets union intersection differenceMathematics

Frequently asked questions

What is the correct answer to this question?

19

Why is this the correct answer?

Every element of B belongs either to the part only in B, B − A, or to the common part A ∩ B. These two regions do not overlap, so their cardinalities can be added: n(B) = n(B − A) + n(A ∩ B) = 13 + 6 = 19. Thus option C is correct. Option B omits the six common elements.

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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