If A ⊆ B ⊆ C, n(C) = 132, n(B) = 84, and n(A) = 37, what is n(C − A)?
Answer and explanation
Correct answer: 95
Because A is a subset of C, every element of A lies inside C. The difference C − A therefore contains all elements of C except the 37 elements belonging to A. Hence n(C − A) = n(C) − n(A) = 132 − 37 = 95. The value 48 would come from subtracting B from C, but the question specifically asks for C − A. The nesting information confirms that the subtraction is valid.
Frequently asked questions
What is the correct answer to this question?
95
Why is this the correct answer?
Because A is a subset of C, every element of A lies inside C. The difference C − A therefore contains all elements of C except the 37 elements belonging to A. Hence n(C − A) = n(C) − n(A) = 132 − 37 = 95. The value 48 would come from subtracting B from C, but the question specifically asks for C − A. The nesting information confirms that the subtraction is valid.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
