If \(n(A\cup B)=75\), \(n(A\cap B)=18\), and \(n(A)=46\), what is the value of \(n(B)\)?
Answer and explanation
Correct answer: 47
For two finite sets, the inclusion-exclusion formula is \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\). Substitute the given values: \(75=46+n(B)-18\). Rearranging gives \(n(B)=75-46+18=47\). The intersection is added back when solving for B because it had been subtracted from the sum of the two set sizes. Thus option A, 47, is the only correct value.
Frequently asked questions
What is the correct answer to this question?
47
Why is this the correct answer?
For two finite sets, the inclusion-exclusion formula is \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\). Substitute the given values: \(75=46+n(B)-18\). Rearranging gives \(n(B)=75-46+18=47\). The intersection is added back when solving for B because it had been subtracted from the sum of the two set sizes. Thus option A, 47, is the only correct value.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
