# Thread: A union B union C

1. ## A union B union C

I need the formula to get the union of A,B,C. For Example. You have set A, set B and Set C. You have all of the information provided to you, other than what the union of all three is.

I have this formula(since i dont know how to input math symbols. int. means intersection):

aUbUc = (a + b + c) - (a int c) - (a int b) - (b int c) + (a int b int c)

would that formula work?

2. If we use $\left| A \right|$ to stand for the number of elements is set $A$ then
$\left| {A \cup B \cup C} \right| = \left| A \right| + \left| B \right| + \left| C \right| - \left| {A \cap B} \right| - \left| {B \cap C} \right| - \left| {A \cap C} \right| + \left| {A \cap B \cap C} \right|$.
That is called the inclusion-exclusion principle.
Do a web search on that topic. There are many generalizations of that idea.