If A = {1, 2, 3}, what is the number of all proper subsets of A?
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Answer and explanation
Correct answer: 7
For a finite set with n elements, every element has two choices in forming a subset: it is either included or excluded. Thus the total number of subsets of A is 2³ = 8. A proper subset is any subset that is not equal to A itself, so we remove the one non-proper subset A. Hence the number of proper subsets is 8 − 1 = 7.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
For a finite set with n elements, every element has two choices in forming a subset: it is either included or excluded. Thus the total number of subsets of A is 2³ = 8. A proper subset is any subset that is not equal to A itself, so we remove the one non-proper subset A. Hence the number of proper subsets is 8 − 1 = 7.
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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