If \(n(U)=120\) and \(n(A')=47\), what is \(n(A)\)?
Answer and explanation
Correct answer: \(73\)
A set and its complement are disjoint and together contain every element of the universal set. Hence, \(n(A)+n(A')=n(U)\). Substituting the given values gives \(n(A)+47=120\), so \(n(A)=120-47=73\). Therefore, option A is correct. The value 47 is the cardinality of the complement, while 120 is the cardinality of the entire universal set, not of \(A\).
Frequently asked questions
What is the correct answer to this question?
\(73\)
Why is this the correct answer?
A set and its complement are disjoint and together contain every element of the universal set. Hence, \(n(A)+n(A')=n(U)\). Substituting the given values gives \(n(A)+47=120\), so \(n(A)=120-47=73\). Therefore, option A is correct. The value 47 is the cardinality of the complement, while 120 is the cardinality of the entire universal set, not of \(A\).
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.
