If A = {p, q} and B = {p, q, r, s}, how many sets X satisfy A ⊂ X ⊆ B?
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Answer and explanation
Correct answer: 3
The condition A ⊂ X ⊆ B means that X must contain p and q, may contain r and s, and must be different from A. The four possible supersets formed from r and s are {p,q}, {p,q,r}, {p,q,s}, and {p,q,r,s}. Since A itself is not allowed by the proper-subset sign, remove {p,q}. Therefore, 4 − 1 = 3 sets satisfy the condition.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
The condition A ⊂ X ⊆ B means that X must contain p and q, may contain r and s, and must be different from A. The four possible supersets formed from r and s are {p,q}, {p,q,r}, {p,q,s}, and {p,q,r,s}. Since A itself is not allowed by the proper-subset sign, remove {p,q}. Therefore, 4 − 1 = 3 sets satisfy the condition.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
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