If \(A=\{0,2,4,6\}\) and \(B=\{1,2,3,4\}\), which statement is false?
Answer and explanation
Correct answer: \(A\cup B=\{2,4\}\)
The intersection consists of common elements, so \(A\cap B=\{2,4\}\). Removing the common elements from \(A\) gives \(A\setminus B=\{0,6\}\), and removing them from \(B\) gives \(B\setminus A=\{1,3\}\). However, the union must contain every distinct element from either set. Thus \(A\cup B=\{0,1,2,3,4,6\}\), not \(\{2,4\}\). Therefore, statement D is false.
Frequently asked questions
What is the correct answer to this question?
\(A\cup B=\{2,4\}\)
Why is this the correct answer?
The intersection consists of common elements, so \(A\cap B=\{2,4\}\). Removing the common elements from \(A\) gives \(A\setminus B=\{0,6\}\), and removing them from \(B\) gives \(B\setminus A=\{1,3\}\). However, the union must contain every distinct element from either set. Thus \(A\cup B=\{0,1,2,3,4,6\}\), not \(\{2,4\}\). Therefore, statement D is false.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
