3. Given the following empty-stack PDA, (15 points) check if the strings ca,ab and would be accepted by this PDA. Show your work in the following three tables, respectively. You need to create/use your own text boxes for your work in the tables. Note that the key here is, whenever the top symbol of the stack is a nonterminal, if the next input symbol to be processed is not a then you put a in front of the un-consumed portion of the input string so you can apply one of the seven instructions of the form " ?,? " to replace the top symbol of the stack with a sequence of terminals and/or nonterminals. \begin{tabular}{|l|} \hline(0,,X) \\ \hline \\ \hline \\ \hline \\ \hline \\ \hline \\ \hline \\ \hline \\ \hline \end{tabular} \begin{tabular}{|} \hline \\ \hline \\ \hline \\ \hline \\ \hline \\ \hline \\ \hline \\ \hline \end{tabular} (2.5 points)