If \(A\subseteq B\), \(n(A)=18\), and \(n(B)=46\), what is \(n(A\cup B)\)?
Answer and explanation
Correct answer: 46
The statement \(A\subseteq B\) means that every element of A is already contained in B. When A is united with B, no new elements are added beyond those already in B; therefore, \(A\cup B=B\). Consequently, \(n(A\cup B)=n(B)=46\). The value 18 is only the cardinality of A, 28 is \(46-18\), the number of elements in \(B\setminus A\), and 64 incorrectly adds the two set sizes without removing the overlap. Hence, option C is correct.
Frequently asked questions
What is the correct answer to this question?
46
Why is this the correct answer?
The statement \(A\subseteq B\) means that every element of A is already contained in B. When A is united with B, no new elements are added beyond those already in B; therefore, \(A\cup B=B\). Consequently, \(n(A\cup B)=n(B)=46\). The value 18 is only the cardinality of A, 28 is \(46-18\), the number of elements in \(B\setminus A\), and 64 incorrectly adds the two set sizes without removing the overlap. Hence, option C 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).
