If A has 5 elements, how many subsets of A are not equal to A?
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Answer and explanation
Correct answer: 31
A set with n elements has 2^n total subsets because each element has two choices: included or excluded. For n = 5, A has 2^5 = 32 subsets. Exactly one of them is A itself. Therefore, the number of subsets not equal to A is 32 − 1 = 31, so option C is correct.
Frequently asked questions
What is the correct answer to this question?
31
Why is this the correct answer?
A set with n elements has 2^n total subsets because each element has two choices: included or excluded. For n = 5, A has 2^5 = 32 subsets. Exactly one of them is A itself. Therefore, the number of subsets not equal to A is 32 − 1 = 31, so 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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