If n(A ∪ B) = n(A), which relation must be true?
Answer and explanation
Correct answer: B ⊆ A
The union A ∪ B contains every element of A and every element of B. If its cardinality is exactly n(A), adding B has not introduced any new element beyond those already in A. Hence every element of B must already belong to A, so B ⊆ A. The sets need not be equal: B may be a proper subset of A. Therefore option A is the only necessary conclusion.
Frequently asked questions
What is the correct answer to this question?
B ⊆ A
Why is this the correct answer?
The union A ∪ B contains every element of A and every element of B. If its cardinality is exactly n(A), adding B has not introduced any new element beyond those already in A. Hence every element of B must already belong to A, so B ⊆ A. The sets need not be equal: B may be a proper subset of A. Therefore option A is the only necessary conclusion.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
