In a situation where a finite set is said to have exactly 5 proper subsets, what is the correct conclusion?
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Answer and explanation
Correct answer: No such finite set exists
For a finite set with n elements, the power set contains 2^n subsets, including the set itself and the empty set. Hence the number of proper subsets is 2^n−1. If this number were 5, then 2^n=6, but 6 is not a power of 2. Thus no finite set can satisfy the stated condition.
Frequently asked questions
What is the correct answer to this question?
No such finite set exists
Why is this the correct answer?
For a finite set with n elements, the power set contains 2^n subsets, including the set itself and the empty set. Hence the number of proper subsets is 2^n−1. If this number were 5, then 2^n=6, but 6 is not a power of 2. Thus no finite set can satisfy the stated condition.
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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