If \(n(U)=55\), \(n(A-B)=14\), \(n(A\cap B)=9\), and \(n(B-A)=17\), what is the number of elements outside \(A\cup B\)?
Answer and explanation
Correct answer: 15
A two-set Venn diagram has three disjoint regions inside the union: the part only in \(A\), the intersection, and the part only in \(B\). These are \(A-B\), \(A\cap B\), and \(B-A\), respectively. Therefore, \(n(A\cup B)=14+9+17=40\). The elements outside both sets are in the complement of the union, so their number is \(n(U)-n(A\cup B)=55-40=15\). Hence option A is correct. The value 40 is the size of the union, not the outside region.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
A two-set Venn diagram has three disjoint regions inside the union: the part only in \(A\), the intersection, and the part only in \(B\). These are \(A-B\), \(A\cap B\), and \(B-A\), respectively. Therefore, \(n(A\cup B)=14+9+17=40\). The elements outside both sets are in the complement of the union, so their number is \(n(U)-n(A\cup B)=55-40=15\). Hence option A is correct. The value 40 is the size of the union, not the outside region.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
