Cardinality Math Example 3

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Example 3

easy
A set SS has 3 elements. How many subsets does SS have? How many proper subsets?

Solution

  1. 1
    A set with nn elements has 2n2^n subsets. Here n=3n=3, so 23=82^3 = 8 subsets.
  2. 2
    A proper subset is any subset except SS itself, so there are 8−1=78 - 1 = 7 proper subsets.

Answer

8 subsets,7 proper subsets8 \text{ subsets},\quad 7 \text{ proper subsets}
Every element is either in a subset or not, giving 2n2^n combinations. Removing SS itself gives the count of proper subsets.

About Cardinality

The cardinality of a finite set is the number of distinct elements it contains, written ∣A∣|A| — it measures the size of the set without regard to element order or identity.

Learn more about Cardinality →

More Cardinality Examples

Example 1 easy

Find the cardinality of: (a) [formula], (b) [formula], (c) [formula].

Example 2 medium

Let [formula] and [formula]. Verify the formula [formula].

Example 4 medium

In a class of 40 students, 25 play football, 20 play basketball, and 10 play both. Use cardinality f

← All Cardinality Examples Cardinality Concept

Related Concepts

SetElement