Identifying Subsets & Power Sets (Intermediate)

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Quizzes Created: 7387 | Total Attempts: 9,527,684
| Questions: 10 | Updated: Nov 12, 2025
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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) Is ∅ ⊂ {∅}?

Explanation

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

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

Explanation

Number of subsets = 2^10 = 1024.

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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

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

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Is ∅ ∈ {∅}?
If A has 5 elements, how many subsets of A have exactly 3 elements?
Is ∅ ⊂ {∅}?
How many subsets does a 6-element set have?
How many proper subsets does a 4-element set have?
How many elements does P(P({a})) have?
If S has 10 elements, how many subsets does it 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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