If A = {a, b, c, d, e}, how many subsets contain the element c?
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Answer and explanation
Correct answer: 16
To count subsets that contain c, keep c fixed in every selected subset. The remaining four elements, a, b, d, and e, may each either be included or excluded independently. Thus there are 2 choices for each of four elements, giving 2^4 = 16 subsets containing c. This is also half of the 2^5 = 32 total subsets.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
To count subsets that contain c, keep c fixed in every selected subset. The remaining four elements, a, b, d, and e, may each either be included or excluded independently. Thus there are 2 choices for each of four elements, giving 2^4 = 16 subsets containing c. This is also half of the 2^5 = 32 total subsets.
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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