Cardinality Math Example 1

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Example 1

easy

Find the cardinality of: (a)

A = \{2, 4, 6, 8, 10\}

, (b)

B = \{x \in \mathbb{N} : x \le 0\}

, (c)

C = \{\{1,2\}, 3, \{4\}\}

Solution

1
(a) Count the distinct elements: $2, 4, 6, 8, 10$ — five elements, so $|A| = 5$ .
2
(b) The only natural number $\le 0$ is $0$ (assuming $0 \in \mathbb{N}$ ). So $B = \{0\}$ and $|B| = 1$ .
3
(c) $C$ has three elements: the set $\{1,2\}$ , the number $3$ , and the set $\{4\}$ . So $|C| = 3$ .

Answer

|A|=5,\quad |B|=1,\quad |C|=3

Cardinality counts distinct top-level elements. When a set contains other sets as elements, each sub-set counts as one element regardless of its own size.

About Cardinality

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

Learn more about Cardinality →

More Cardinality Examples

Example 2 medium

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

Example 3 easy

A set [formula] has 3 elements. How many subsets does [formula] have? How many proper subsets?

Example 4 medium

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

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Related Concepts

Set Element