If \(A\setminus B=\{1,4\}\), \(A\cap B=\{2,3\}\), and \(B\setminus A=\{5,6,7\}\), what is \(A\cup B\)?
Answer and explanation
Correct answer: \(\{1,2,3,4,5,6,7\}\)
Every element of the union belongs to exactly one of three disjoint regions: \(A\setminus B\), \(A\cap B\), or \(B\setminus A\). Combining the given regions gives \(\{1,4\}\cup\{2,3\}\cup\{5,6,7\}=\{1,2,3,4,5,6,7\}\). Therefore option A is correct. The other options omit one of the three regions.
Frequently asked questions
What is the correct answer to this question?
\(\{1,2,3,4,5,6,7\}\)
Why is this the correct answer?
Every element of the union belongs to exactly one of three disjoint regions: \(A\setminus B\), \(A\cap B\), or \(B\setminus A\). Combining the given regions gives \(\{1,4\}\cup\{2,3\}\cup\{5,6,7\}=\{1,2,3,4,5,6,7\}\). Therefore option A is correct. The other options omit one of the three regions.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
