If \(n(A-B)=16\) and \(n(A\cap B)=11\), what is \(n(A)\)?
Answer and explanation
Correct answer: 27
Every element of A is either exclusive to A, belonging to \(A-B\), or common to both sets, belonging to \(A\cap B\). These two parts are disjoint and together form A. Thus, \(n(A)=n(A-B)+n(A\cap B)=16+11=27\). Option C is correct; 16 counts only the exclusive portion and does not include the shared elements.
Frequently asked questions
What is the correct answer to this question?
27
Why is this the correct answer?
Every element of A is either exclusive to A, belonging to \(A-B\), or common to both sets, belonging to \(A\cap B\). These two parts are disjoint and together form A. Thus, \(n(A)=n(A-B)+n(A\cap B)=16+11=27\). Option C is correct; 16 counts only the exclusive portion and does not include the shared 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).
