For two sets A and B, which of the following conditions is equivalent to A ⊆ B?
Answer and explanation
Correct answer: A ∩ B = A
The statement A ⊆ B means that every element of A is also an element of B. Consequently, taking the intersection of A and B leaves every element of A and no additional element, so A ∩ B = A. Conversely, if A ∩ B = A, every element of A lies in B, which proves A ⊆ B. Option B instead represents B ⊆ A; option C means A and B are disjoint; and option D represents A ⊆ B only in a different difference condition, not the stated equivalence.
Frequently asked questions
What is the correct answer to this question?
A ∩ B = A
Why is this the correct answer?
The statement A ⊆ B means that every element of A is also an element of B. Consequently, taking the intersection of A and B leaves every element of A and no additional element, so A ∩ B = A. Conversely, if A ∩ B = A, every element of A lies in B, which proves A ⊆ B. Option B instead represents B ⊆ A; option C means A and B are disjoint; and option D represents A ⊆ B only in a different difference condition, not the stated equivalence.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
