If A and B are finite sets, A is a proper subset of B, and n(A) = 6, which value of n(B) is impossible?
Answer and explanation
Correct answer: 6
A proper subset of B means that every element of A belongs to B, but A and B are not equal. For finite sets, this necessarily gives n(A) < n(B). Since n(A) = 6, B must contain at least one additional element and therefore must have more than six elements. Hence n(B) = 6 is impossible. Values 7, 8, and 10 are all possible because B can be formed by adding one, two, or four new elements to A, respectively.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
A proper subset of B means that every element of A belongs to B, but A and B are not equal. For finite sets, this necessarily gives n(A) < n(B). Since n(A) = 6, B must contain at least one additional element and therefore must have more than six elements. Hence n(B) = 6 is impossible. Values 7, 8, and 10 are all possible because B can be formed by adding one, two, or four new elements to A, respectively.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
