Set operations

Set Union (A U B)

Contains all elements in EITHER A or B.

Example:

Intersection (A $\cap$ B)

Contains all the elements in BOTH A and B.

$A\ \cap B = \{ x|x \in A\ and\ x\ \in B \}$

Set difference (A - B)

Contains the elements that are in A but not in B.

$A\ -\ B\ = \{ x|x \in A\ and\ x \notin B \}$

Symmetric difference (A (+) B)

Contains the elements that are in A or in B but not in both.

$A\ (+)\ B\ = \{ x\ |\ (x \in A\ OR\ x \in B)\ and\ x\ \notin A\ \cap B \}$

$A (+) B = (A \cup B) - (A \cap B)$

Example exercise

Given two sets A = {1, 2, 3} and B = {3, 4, 5}:

• Union: { 1, 2, 3, 4, 5}

• Intersection: {3}

• Difference: { 1, 2}

• Symmetric difference: {1, 2, 4, 5}