Identifying Subsets & Power Sets (Intermediate)

  • 11th Grade
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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: 27 | Questions: 10 | Updated: Jan 21, 2026
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Question 1 / 11
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1) Is ∅ ∈ {∅}?

Explanation

{∅} is a set with one element, and that element is ∅.

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

As sets grow, so do their subsets! In this quiz, you’ll handle larger sets and more complex power set problems. Take this quiz to practice careful counting and precise set organization.

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2) If A has 5 elements, how many subsets of A have exactly 3 elements?

Explanation

Choose 3 elements out of 5: (5 choose 3) = 10.

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3) How many subsets does a 6-element set have?

Explanation

Number of subsets = 2^n. For n=6, 2^6 = 64.

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4) If S has 10 elements, how many subsets does it have?

Explanation

Number of subsets = 2^10 = 1024.

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

Explanation

Proper subsets = 2^n − 1. For n=4, 2^4 − 1 = 15.

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6) Is {∅} ⊂ ∅?

Explanation

∅ has no elements, but {∅} has one element (the empty set itself), so it cannot be a subset.

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7) How many elements does P(P({a})) have?

Explanation

P({a}) = {∅, {a}} has 2 elements. Its power set has 2^2 = 4 elements.

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8) If A ⊂ B and B has 8 elements, what is the maximum number of elements A can have?

Explanation

A proper subset must have fewer elements than B. So maximum is 7.

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9) How many 2-element subsets does a set with 7 elements have?

Explanation

Choose 2 elements out of 7: (7 choose 2) = 21.

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10) Is ∅ ⊂ {∅}?

Explanation

The empty set is a subset of every set, including {∅}.

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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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Is ∅ ∈ {∅}?
If A has 5 elements, how many subsets of A have exactly 3 elements?
How many subsets does a 6-element set have?
If S has 10 elements, how many subsets does it have?
How many proper subsets does a 4-element set have?
Is {∅} ⊂ ∅?
How many elements does P(P({a})) have?
If A ⊂ B and B has 8 elements, what is the maximum number of...
How many 2-element subsets does a set with 7 elements have?
Is ∅ ⊂ {∅}?
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