Let \(U_1=\{1,2,3,4\}\), \(U_2=\{1,2,3,4,5,6\}\), and \(A=\{1,2\}\). What is the set difference between the complement of \(A\) relative to \(U_2\) and the complement of \(A\) relative to \(U_1\), taking the former difference from the latter?
Answer and explanation
Correct answer: \(\{5,6\}\)
A complement depends on the universal set being used. Relative to \(U_2\), the complement of \(A\) is \(U_2\setminus A=\{3,4,5,6\}\). Relative to \(U_1\), it is \(U_1\setminus A=\{3,4\}\). Taking the first complement minus the second gives \(\{3,4,5,6\}\setminus\{3,4\}=\{5,6\}\). Hence option A is correct. The result shows why the universal set must always be specified.
Frequently asked questions
What is the correct answer to this question?
\(\{5,6\}\)
Why is this the correct answer?
A complement depends on the universal set being used. Relative to \(U_2\), the complement of \(A\) is \(U_2\setminus A=\{3,4,5,6\}\). Relative to \(U_1\), it is \(U_1\setminus A=\{3,4\}\). Taking the first complement minus the second gives \(\{3,4,5,6\}\setminus\{3,4\}=\{5,6\}\). Hence option A is correct. The result shows why the universal set must always be specified.
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.
