If A = {x, y, z}, how many elements of P(A) are also proper subsets of A?
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Answer and explanation
Correct answer: 7
A has three elements, so its power set contains 2³ = 8 subsets. Every subset of A belongs to P(A), but a proper subset must not be equal to A itself. Exactly one subset, namely {x,y,z}, is not proper. Removing it from the eight subsets leaves 8 − 1 = 7 proper subsets. Therefore option C is correct.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
A has three elements, so its power set contains 2³ = 8 subsets. Every subset of A belongs to P(A), but a proper subset must not be equal to A itself. Exactly one subset, namely {x,y,z}, is not proper. Removing it from the eight subsets leaves 8 − 1 = 7 proper subsets. Therefore option C is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
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