If A = {1, 2, 3, 4}, how many subsets of A do not contain 1?
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Answer and explanation
Correct answer: 8
A subset that does not contain 1 can use only the remaining elements {2, 3, 4}. Each of these three elements has two independent choices: it may either be included or excluded. Therefore, the number of permitted subsets is 2^3 = 8. Equivalently, these are all subsets of A − {1}, including the empty set and {2, 3, 4}.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
A subset that does not contain 1 can use only the remaining elements {2, 3, 4}. Each of these three elements has two independent choices: it may either be included or excluded. Therefore, the number of permitted subsets is 2^3 = 8. Equivalently, these are all subsets of A − {1}, including the empty set and {2, 3, 4}.
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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