If A ⊆ B, n(A) = 8, and B has no element outside A, which conclusion must be true?
Answer and explanation
Correct answer: A = B
The statement A ⊆ B says that every element of A belongs to B. The additional statement that B has no element outside A says that every element of B belongs to A, or B ⊆ A. Thus both inclusions hold: A ⊆ B and B ⊆ A. By the criterion for equality of sets, A = B. The value n(A) = 8 is consistent with this and also implies n(B) = 8, not 16. Hence option A is certain.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
The statement A ⊆ B says that every element of A belongs to B. The additional statement that B has no element outside A says that every element of B belongs to A, or B ⊆ A. Thus both inclusions hold: A ⊆ B and B ⊆ A. By the criterion for equality of sets, A = B. The value n(A) = 8 is consistent with this and also implies n(B) = 8, not 16. Hence option A is certain.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
