Discrete Mathematics · Quick Reference

Sets Cheat Sheet

Discrete Mathematics · Lesson 2/9

In one line: a set is simply a well-defined collection of distinct objects. Sets form the basic language used to describe and organize almost every other area of mathematics.

Key Ideas

1Set Notation. A set is written with curly braces, like A = {1,2,3}. An element x belonging to set A is written 'x is in A'.

2Subset. Set A is a subset of B if every element of A is also in B, written 'A is a subset of B'.

3Union (A union B). The set containing every element that is in A, in B, or in both.

4Intersection (A intersection B). The set containing only the elements that are in both A and B.

5Complement and Empty Set. The complement of A contains everything in the universal set that is NOT in A. The empty set (written as {} or the empty-set symbol) contains no elements at all.

Worked Examples

Let A = {1,2,3,4} and B = {3,4,5,6}. Find A union B.

A union B = {1,2,3,4,5,6}

Using the same sets, find A intersection B.

A intersection B = {3,4}

Using |A|=4, |B|=4, |A intersection B|=2, find |A union B|.

|A union B| = 6

Formulas

|A union B| = |A| + |B| - |A intersection B|

Practice Yourself

Let A={1,2,3}, B={2,3,4}. Find A union B.

{1,2,3,4}

Let A={1,2,3}, B={2,3,4}. Find A intersection B.

{2,3}

Is {1,2} a subset of {1,2,3}?

Yes