If A ⊆ B, n(A) = 6, and n(B) = 6, what is certain about A and B?
Advertisement
Answer and explanation
Correct answer: A = B
When A is a subset of B, every element of A is already contained in B. If B had even one additional element, its cardinality would be greater than that of A. Since both finite sets have cardinality 6, B cannot contain any extra element. Therefore the two sets contain exactly the same elements, so A = B.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
When A is a subset of B, every element of A is already contained in B. If B had even one additional element, its cardinality would be greater than that of A. Since both finite sets have cardinality 6, B cannot contain any extra element. Therefore the two sets contain exactly the same elements, so A = B.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
Advertisement