If A ⊂ B and B − A = {9}, how many sets X satisfy A ⊆ X ⊆ B?
Answer and explanation
Correct answer: 2
The condition A ⊆ X ⊆ B means that every element of A must be in X, while the only element that can be added beyond A is 9, because B − A = {9}. Therefore there are exactly two possibilities: X = A, when 9 is excluded, or X = A ∪ {9} = B, when 9 is included. Equivalently, the number is 2 raised to the number of optional elements: 2¹ = 2. Hence option B is correct.
Frequently asked questions
What is the correct answer to this question?
2
Why is this the correct answer?
The condition A ⊆ X ⊆ B means that every element of A must be in X, while the only element that can be added beyond A is 9, because B − A = {9}. Therefore there are exactly two possibilities: X = A, when 9 is excluded, or X = A ∪ {9} = B, when 9 is included. Equivalently, the number is 2 raised to the number of optional elements: 2¹ = 2. Hence option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
