If A = {x : x ∈ N, x ≤ 4}, how many subsets of A contain 4?
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Answer and explanation
Correct answer: 8
Taking N = {1, 2, 3, ...}, the condition x ≤ 4 gives A = {1, 2, 3, 4}. Since 4 must be included, it is fixed. Each of the remaining three elements, 1, 2, and 3, can independently be included or omitted. Therefore the number of valid subsets is 2³ = 8.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
Taking N = {1, 2, 3, ...}, the condition x ≤ 4 gives A = {1, 2, 3, 4}. Since 4 must be included, it is fixed. Each of the remaining three elements, 1, 2, and 3, can independently be included or omitted. Therefore the number of valid subsets is 2³ = 8.
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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