If A = {1, 2, 3, 4}, how many subsets contain the element 1?
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Answer and explanation
Correct answer: 8
To form a subset that must contain 1, fix 1 as included. Each of the remaining three elements, 2, 3, and 4, has two independent choices: it may be included or omitted. Hence the number of subsets is 2 × 2 × 2 = 2^3 = 8. The value 16 counts every subset of A, including those without 1.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
To form a subset that must contain 1, fix 1 as included. Each of the remaining three elements, 2, 3, and 4, has two independent choices: it may be included or omitted. Hence the number of subsets is 2 × 2 × 2 = 2^3 = 8. The value 16 counts every subset of A, including those without 1.
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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