If \(A=\{1,2,3,4\}\), what are \(A\cup\varnothing\), \(A\cap\varnothing\), and \(A-\varnothing\), respectively?
Answer and explanation
Correct answer: \((A,\varnothing,A)\)
The empty set has no elements. Therefore, taking the union of \(A\) with the empty set adds nothing, so \(A\cup\varnothing=A\). Their intersection has no common element, so \(A\cap\varnothing=\varnothing\). Subtracting the empty set removes nothing, giving \(A-\varnothing=A\). Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
\((A,\varnothing,A)\)
Why is this the correct answer?
The empty set has no elements. Therefore, taking the union of \(A\) with the empty set adds nothing, so \(A\cup\varnothing=A\). Their intersection has no common element, so \(A\cap\varnothing=\varnothing\). Subtracting the empty set removes nothing, giving \(A-\varnothing=A\). Hence 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).
