Practice Cardinality in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The cardinality of a set is the number of distinct elements it contains, written |A| or n(A).
Cardinality answers "how many?" — count each distinct element once and you have the cardinality.
Example 1
easyFind 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\}\}.
Example 2
mediumLet A = \{1,2,3,4\} and B = \{3,4,5,6\}. Verify the formula |A \cup B| = |A| + |B| - |A \cap B|.
Example 3
easyA set S has 3 elements. How many subsets does S have? How many proper subsets?
Example 4
mediumIn a class of 40 students, 25 play football, 20 play basketball, and 10 play both. Use cardinality formulas to find how many play at least one sport and how many play neither.