Identifying Subsets & Power Sets (Advanced)

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Cierra Henderson, MBA |
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Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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| Attempts: 15 | Questions: 10 | Updated: Jan 21, 2026
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1) If A has n elements, how many elements does P(P(A)) have?

Explanation

The power set of A has 2^n elements. Taking its power set gives 2^(2^n).

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About This Quiz
Identifying Subsets & Power Sets (Advanced) - Quiz

Ready for a challenge? This quiz pushes your skills with advanced subset and power set problems, requiring both strategy and accuracy. Try this quiz to test your mastery of these set operations.

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2) A has 3 elements. How many elements are in P(P(P(A)))?

Explanation

|A|=3 → P(A) has 2^3=8. → P(P(A)) has 2^8=256. → P(P(P(A))) has 2^256.

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3) If X ⊂ Y and |Y| = n, how many subsets of Y contain X?

Explanation

Every element not in X can either be included or excluded freely → 2^(n−|X|).

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4) How many proper subsets does a 7-element set have?

Explanation

Total subsets = 2^7=128. Proper subsets exclude the set itself → 127.

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5) If P(A) has 16 elements, how many elements does A have?

Explanation

|P(A)|=2^|A|=16. So |A|=4.

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6) If |P(A)| = 512, find |A|.

Explanation

2^|A|=512 → |A|=9.

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7) For set B={1,2,{3}}, how many subsets does B have?

Explanation

B has 3 elements (1,2,{3}). Subsets=2^3=8.

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8) If S has n elements, how many subsets of S have odd cardinality?

Explanation

Half of all subsets have odd cardinality → 2^(n−1).

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9) How many subsets of a 10-element set have at least one element?

Explanation

Total subsets = 2^10=1024. Excluding ∅ leaves 1023.

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10) How many subsets of a 6-element set have exactly 4 elements?

Explanation

Number of 4-element subsets = C(6,4)=15.

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Cierra Henderson |MBA |
K-12 Expert
Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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If A has n elements, how many elements does P(P(A)) have?
A has 3 elements. How many elements are in P(P(P(A)))?
If X ⊂ Y and |Y| = n, how many subsets of Y contain X?
How many proper subsets does a 7-element set have?
If P(A) has 16 elements, how many elements does A have?
If |P(A)| = 512, find |A|.
For set B={1,2,{3}}, how many subsets does B have?
If S has n elements, how many subsets of S have odd cardinality?
How many subsets of a 10-element set have at least one element?
How many subsets of a 6-element set have exactly 4 elements?
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