If \(A=\{1,2,3\}\), what is \(A\cup\varnothing\)?
Answer and explanation
Correct answer: \(\{1,2,3\}\)
The empty set \(\varnothing\) contains no elements. Therefore, taking the union of \(A\) with the empty set adds nothing to \(A\), and the result remains unchanged: \(A\cup\varnothing=A\). Since \(A=\{1,2,3\}\), the answer is \(\{1,2,3\}\). This is called the identity property of union; it should not be confused with intersection with the empty set, which is empty.
Frequently asked questions
What is the correct answer to this question?
\(\{1,2,3\}\)
Why is this the correct answer?
The empty set \(\varnothing\) contains no elements. Therefore, taking the union of \(A\) with the empty set adds nothing to \(A\), and the result remains unchanged: \(A\cup\varnothing=A\). Since \(A=\{1,2,3\}\), the answer is \(\{1,2,3\}\). This is called the identity property of union; it should not be confused with intersection with the empty set, which is empty.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
