If A ⊆ B, n(A) = 4, n(B) = 4, and both sets are finite, which statement is correct?
Answer and explanation
Correct answer: A = B
For finite sets, if A ⊆ B, then every element of A is already in B. If B had even one additional element, its cardinality would be greater than that of A. Here both sets have cardinality 4, so B cannot contain any extra element. Consequently, A and B contain exactly the same elements and are equal. Option B is false because the inclusion is not proper, option C is false because B − A is empty, and option D is false because their intersection is A, not the empty set.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
For finite sets, if A ⊆ B, then every element of A is already in B. If B had even one additional element, its cardinality would be greater than that of A. Here both sets have cardinality 4, so B cannot contain any extra element. Consequently, A and B contain exactly the same elements and are equal. Option B is false because the inclusion is not proper, option C is false because B − A is empty, and option D is false because their intersection is A, not the empty set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
