Identifying Subsets & Power Sets (Intermediate)

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1) 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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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) 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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3) Is ∅ ⊂ {∅}?

Explanation

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

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4) Is ∅ ∈ {∅}?

Explanation

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

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5) Is {∅} ⊂ ∅?

Explanation

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

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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) 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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10) 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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How many subsets does a 6-element set have?
How many proper subsets does a 4-element set have?
Is ∅ ⊂ {∅}?
Is ∅ ∈ {∅}?
Is {∅} ⊂ ∅?
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...
If A has 5 elements, how many subsets of A have exactly 3 elements?
How many 2-element subsets does a set with 7 elements have?
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