If A = {x ∈ N : x ≤ 4}, what is the number of subsets of A?
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Answer and explanation
Correct answer: 16
Taking N to mean the positive natural numbers, A = {1, 2, 3, 4}, so A has four elements. A set with n elements has exactly 2^n subsets, because each element has two independent choices: it may be included or excluded. Hence the number of subsets is 2^4 = 16. This count includes both the empty set and A itself.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
Taking N to mean the positive natural numbers, A = {1, 2, 3, 4}, so A has four elements. A set with n elements has exactly 2^n subsets, because each element has two independent choices: it may be included or excluded. Hence the number of subsets is 2^4 = 16. This count includes both the empty set and A itself.
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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