If a finite set A 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
If a finite set A has n elements, then its total number of subsets is 2^n, and its number of proper subsets is 2^n − 1. Equating this to 5 gives 2^n = 6. Since 6 is not a power of 2, no non-negative integer n satisfies the equation. Therefore, no such finite set exists.
Frequently asked questions
What is the correct answer to this question?
No such finite set exists
Why is this the correct answer?
If a finite set A has n elements, then its total number of subsets is 2^n, and its number of proper subsets is 2^n − 1. Equating this to 5 gives 2^n = 6. Since 6 is not a power of 2, no non-negative integer n satisfies the equation. Therefore, no such finite set exists.
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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