For any given finite set LaTeX: SS, let LaTeX: n\left(S\right)n ( S ) denote the number of elements it contains. Given any two finite sets LaTeX: AA and LaTeX: BB 1. Prove that LaTeX: n\left(A\cup B\right)=n\left(A\right)+n\left(B\r ight)-n\left(A\cap B\right)n ( A ∪ B ) = n ( A ) + n ( B ) − n ( A ∩ B ) 2. Determine the corresponding formula for LaTeX: n\left(A\cup B\cup C\right)n ( A ∪ B ∪ C ), where LaTeX: A,\:B,\:\text{and}\:CA , B , and C are finite sets