If A ⊆ B ⊆ C, n(C) = 118, n(B) = 73, and n(A) = 29, what is n(C − A)?
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Answer and explanation
Correct answer: 89
Because A ⊆ B ⊆ C, every element of A is also an element of C. The set C − A therefore contains all elements of C except those belonging to A. Hence, n(C − A) = n(C) − n(A) = 118 − 29 = 89. The value of n(B) is not needed for this particular difference, although it confirms the nested relationship.
Frequently asked questions
What is the correct answer to this question?
89
Why is this the correct answer?
Because A ⊆ B ⊆ C, every element of A is also an element of C. The set C − A therefore contains all elements of C except those belonging to A. Hence, n(C − A) = n(C) − n(A) = 118 − 29 = 89. The value of n(B) is not needed for this particular difference, although it confirms the nested relationship.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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