If \(A\cap B=\varnothing\), \(n(A)=24\), and \(n(B)=37\), what is \(n(A\cup B)\)?
Answer and explanation
Correct answer: 61
Since \(A\cap B=\varnothing\), the sets are disjoint and have no common elements. Therefore, every element in A and every element in B is counted exactly once in their union. The cardinality rule is \(n(A\cup B)=n(A)+n(B)\). Hence, \(n(A\cup B)=24+37=61\). Options 24 and 37 represent the sizes of the individual sets, not their union, while 13 has no basis in the given information. Thus, option D is correct.
Frequently asked questions
What is the correct answer to this question?
61
Why is this the correct answer?
Since \(A\cap B=\varnothing\), the sets are disjoint and have no common elements. Therefore, every element in A and every element in B is counted exactly once in their union. The cardinality rule is \(n(A\cup B)=n(A)+n(B)\). Hence, \(n(A\cup B)=24+37=61\). Options 24 and 37 represent the sizes of the individual sets, not their union, while 13 has no basis in the given information. Thus, option D 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).
