If A ⊂ B and n(B) = 7, which value is impossible for n(A)?
Answer and explanation
Correct answer: 7
The symbol A ⊂ B denotes a proper subset, so A is contained in B but is not equal to B. For finite sets, a proper subset must have strictly fewer elements than the original set. Since B has 7 elements, n(A) may be 0, 4, or 6, depending on the subset, but it cannot be 7. If n(A) were 7, A and B would have equal finite cardinality and would be equal, contradicting A ⊂ B. Thus option D is impossible.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
The symbol A ⊂ B denotes a proper subset, so A is contained in B but is not equal to B. For finite sets, a proper subset must have strictly fewer elements than the original set. Since B has 7 elements, n(A) may be 0, 4, or 6, depending on the subset, but it cannot be 7. If n(A) were 7, A and B would have equal finite cardinality and would be equal, contradicting A ⊂ B. Thus option D is impossible.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
