If A = {a, b, c, d, e}, how many subsets in P(A) contain a and contain neither b nor c?
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Answer and explanation
Correct answer: 4
The element a must be included, so it has only one fixed choice. The elements b and c must be excluded, so they also have no choice. Only d and e remain unrestricted; each may either be included or excluded independently. Thus the number of possible subsets is 2×2 = 2^2 = 4.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The element a must be included, so it has only one fixed choice. The elements b and c must be excluded, so they also have no choice. Only d and e remain unrestricted; each may either be included or excluded independently. Thus the number of possible subsets is 2×2 = 2^2 = 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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