AMC 8 2008 Problem 11

Each of the $39$ students in the eighth grade at Lincoln Middle School has one dog or one cat or both a dog and a cat. Twenty students have a dog and $26$ students have a cat. How many students have both a dog and a cat? $\textbf{(A)}\ 7 \textbf{(B)}\ 13 \textbf{(C)}\ 19 \textbf{(D)}\ 39 \textbf{(E)}\ 46$