Identifying Subsets & Power Sets (Advanced)

Reviewed by Editorial Team
The ProProfs editorial team is comprised of experienced subject matter experts. They've collectively created over 10,000 quizzes and lessons, serving over 100 million users. Our team includes in-house content moderators and subject matter experts, as well as a global network of rigorously trained contributors. All adhere to our comprehensive editorial guidelines, ensuring the delivery of high-quality content.
Learn about Our Editorial Process
| By Thames
T
Thames
Community Contributor
Quizzes Created: 7387 | Total Attempts: 9,527,684
| Questions: 10 | Updated: Nov 12, 2025
Please wait...
Question 1 / 10
0 %
0/100
Score 0/100
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).

Submit
Please wait...
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.

2)
You may optionally provide this to label your report, leaderboard, or certificate.
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.

Submit
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|).

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

Explanation

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

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

Explanation

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

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

Explanation

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

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

Explanation

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

Submit
8) If |P(A)| = 512, find |A|.

Explanation

2^|A|=512 → |A|=9.

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

Explanation

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

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

Explanation

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

Submit
×
Saved
Thank you for your feedback!
10)
Your input helps us improve, and you’ll get your detailed results next.
View My Results
Cancel
  • All
    All (10)
  • Unanswered
    Unanswered ()
  • Answered
    Answered ()
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 subsets of a 10-element set have at least one element?
How many proper subsets does a 7-element set have?
How many subsets of a 6-element set have exactly 4 elements?
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?
Alert!

Advertisement