If \(n(U)=50\) and \(n(A')=22\), find \(n(A)\).
Answer and explanation
Correct answer: 28
A set and its complement are disjoint, and their union is the universal set. Consequently, their cardinalities satisfy \(n(A)+n(A')=n(U)\). Using the given values, \(n(A)+22=50\), so \(n(A)=50-22=28\). The number 22 counts the elements of the complement, while 50 counts all elements of the universal set. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
28
Why is this the correct answer?
A set and its complement are disjoint, and their union is the universal set. Consequently, their cardinalities satisfy \(n(A)+n(A')=n(U)\). Using the given values, \(n(A)+22=50\), so \(n(A)=50-22=28\). The number 22 counts the elements of the complement, while 50 counts all elements of the universal set. Therefore, option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
