Cardinality Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium

Let

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

and

B = \{3,4,5,6\}

. Verify the formula

|A \cup B| = |A| + |B| - |A \cap B|

Solution

1
Compute: $|A| = 4$ , $|B| = 4$ .
2
Find $A \cap B = \{3,4\}$ , so $|A \cap B| = 2$ .
3
By the formula: $|A \cup B| = 4 + 4 - 2 = 6$ .
4
Verify directly: $A \cup B = \{1,2,3,4,5,6\}$ which has 6 elements. Confirmed.

Answer

|A \cup B| = 6

The inclusion-exclusion formula corrects for double-counting elements in

A \cap B

. Verifying by direct count confirms the formula works.

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 1 easy

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

← All Cardinality Examples Cardinality Concept

Related Concepts

Set Element