If A = {1, 2, 3}, what is A ∩ ∅?
Answer and explanation
Correct answer: ∅
The intersection of two sets consists of elements common to both sets. Although A contains 1, 2, and 3, the empty set ∅ contains no elements at all. Therefore, there cannot be any element common to A and ∅, and A ∩ ∅ = ∅. Options A and B incorrectly treat intersection like union, while option D invents an element that is not present in either set. This is the empty-set property of intersection and is valid for every set A.
Frequently asked questions
What is the correct answer to this question?
∅
Why is this the correct answer?
The intersection of two sets consists of elements common to both sets. Although A contains 1, 2, and 3, the empty set ∅ contains no elements at all. Therefore, there cannot be any element common to A and ∅, and A ∩ ∅ = ∅. Options A and B incorrectly treat intersection like union, while option D invents an element that is not present in either set. This is the empty-set property of intersection and is valid for every set A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
