If a set has 32 total subsets, how many proper subsets does it have?
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Answer and explanation
Correct answer: 31
For a finite set with n elements, the total number of subsets is 2^n. A proper subset is a subset that is not equal to the original set. Among all 32 subsets, exactly one subset is the original set itself. Hence the number of proper subsets is 32 − 1 = 31. The empty set is included among the proper subsets.
Frequently asked questions
What is the correct answer to this question?
31
Why is this the correct answer?
For a finite set with n elements, the total number of subsets is 2^n. A proper subset is a subset that is not equal to the original set. Among all 32 subsets, exactly one subset is the original set itself. Hence the number of proper subsets is 32 − 1 = 31. The empty set is included among the proper subsets.
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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