If \(A=\{4,5,6\}\), what is \(A\cap\varnothing\)?
Answer and explanation
Correct answer: \(\varnothing\)
An intersection contains elements common to both sets. The empty set \(\varnothing\) has no elements at all, so there cannot be any element common to \(A=\{4,5,6\}\) and \(\varnothing\). Therefore, \(A\cap\varnothing=\varnothing\). Notice that this differs from union with the empty set: \(A\cup\varnothing=A\), whereas intersection with it always produces the empty set.
Frequently asked questions
What is the correct answer to this question?
\(\varnothing\)
Why is this the correct answer?
An intersection contains elements common to both sets. The empty set \(\varnothing\) has no elements at all, so there cannot be any element common to \(A=\{4,5,6\}\) and \(\varnothing\). Therefore, \(A\cap\varnothing=\varnothing\). Notice that this differs from union with the empty set: \(A\cup\varnothing=A\), whereas intersection with it always produces the empty set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
