If A, B, and C satisfy A ⊆ B ⊆ C, then (C − A) − (B − A) is equal to which set?
Answer and explanation
Correct answer: C − B
Because A is a subset of B, every element of B − A is also an element of C − A. Starting with C − A means retaining elements of C that are not in A. Removing B − A then removes all elements that are in B but not in A. The elements left are precisely those in C that are outside B, namely C − B. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
C − B
Why is this the correct answer?
Because A is a subset of B, every element of B − A is also an element of C − A. Starting with C − A means retaining elements of C that are not in A. Removing B − A then removes all elements that are in B but not in A. The elements left are precisely those in C that are outside B, namely C − B. Hence option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
