If A ∩ B = A, which of the following conclusions is always true?
Answer and explanation
Correct answer: A ⊆ B
The equation A ∩ B = A means that intersecting A with B removes no element from A. Hence every element of A must already be in B. More formally, if x ∈ A, then x belongs to A ∩ B because that intersection equals A; therefore x ∈ B. Thus A ⊆ B. The reverse inclusion is not guaranteed, and the remaining choices require conditions that are not supplied.
Frequently asked questions
What is the correct answer to this question?
A ⊆ B
Why is this the correct answer?
The equation A ∩ B = A means that intersecting A with B removes no element from A. Hence every element of A must already be in B. More formally, if x ∈ A, then x belongs to A ∩ B because that intersection equals A; therefore x ∈ B. Thus A ⊆ B. The reverse inclusion is not guaranteed, and the remaining choices require conditions that are not supplied.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
