If \(n(A)=18\), \(n(B)=25\), and \(n(A\cup B)=25\), then what is \(n(A\setminus B)\)?
Answer and explanation
Correct answer: 0
Use the cardinality formula \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\). Substituting the given values gives \(25=18+25-n(A\cap B)\), so \(n(A\cap B)=18\). Thus every one of the 18 elements of \(A\) is also in \(B\), meaning \(A\subseteq B\). Therefore \(A\setminus B\) is empty and its cardinality is 0. Option A is correct.
Frequently asked questions
What is the correct answer to this question?
0
Why is this the correct answer?
Use the cardinality formula \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\). Substituting the given values gives \(25=18+25-n(A\cap B)\), so \(n(A\cap B)=18\). Thus every one of the 18 elements of \(A\) is also in \(B\), meaning \(A\subseteq B\). Therefore \(A\setminus B\) is empty and its cardinality is 0. Option A 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).
