Card (X U Y) = Card (X) + Card (Y) - Card(X inter Y)

\(Temos: \\ X = (X\diagdown Y)\cup (X\cap Y) \\ \Rightarrow Card X = Card (X\diagdown Y) + Card(X\cup Y) \\ \Rightarrow Card (X\diagdown Y) = Card X - Card(X\cup Y) \\ Por\, outro\, lado: \\ (X\cup Y) = (X\diagdown Y) \cup Y \\ \Rightarrow Card(X\cup Y) = Card(X\diagdown Y) + Card Y \\ \Rightarrow Card(X\cup Y) = Card X + Card Y - Card(X\cap Y) \\ C.Q.D. \)