Calculate set cardinality, unions, intersections, complements, power sets, and Cartesian products from set elements or counts in one place.

Enter finite sets. Use {} for an empty set.

Second set, universe and parsing

Blank omits B in element mode; {} supplies an empty set.

Blank omits element complements. U must contain A and any supplied B.

Blank omits count complements; must match a supplied U list.

Set Cardinality Formula

The following formula is used to calculate the cardinality of a set.

C = |S|

Variables:

  • C is the cardinality of the set
  • S is the set

To calculate the cardinality of a set, count the distinct elements in the set; repeated entries count once. The cardinality of a set is represented by the symbol “|S|”, where “S” is the set.

What is a Set Cardinality?

Set cardinality refers to the number of elements that are contained in a set. In other words, it is a measure of the “size” of a set. For finite sets, the cardinality is simply a count of all its elements. For infinite sets, the concept of cardinality becomes more complex and is defined in terms of a one-to-one correspondence between the elements of the set and the elements of other sets.

How to Calculate Set Cardinality?

The following steps outline how to calculate the Set Cardinality.

  1. First, determine the set (S).
  2. Next, count the number of elements in the set (C).
  3. Finally, calculate the Set Cardinality.
  4. After counting the elements, check your answer with the formula above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Set (S) = {1, 2, 3, 4, 5}

Cardinality of the set (C) = |S| = 5