If A = {2, 4, 6, 8} and B = {1, 2, 3, 4}, which statement about A ∩ B ⊆ A ∪ B is correct?
Answer and explanation
Correct answer: It is always true
Every element of A ∩ B belongs to both A and B. Since the union A ∪ B contains every element that belongs to at least one of the two sets, every element of the intersection must also be in the union. Therefore A ∩ B is always a subset of A ∪ B, regardless of whether the sets are equal, disjoint, finite, or empty.
Frequently asked questions
What is the correct answer to this question?
It is always true
Why is this the correct answer?
Every element of A ∩ B belongs to both A and B. Since the union A ∪ B contains every element that belongs to at least one of the two sets, every element of the intersection must also be in the union. Therefore A ∩ B is always a subset of A ∪ B, regardless of whether the sets are equal, disjoint, finite, or 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).
