Ren Descartes was a seventeenth-century French mathematician and philosopher. One of his most memorable statements is, I

René Descartes was a seventeenth-century French mathematician and philosopher. One of his most memorable statements is, “I think, therefore, I am.” This statement is the basis for the following joke.

Descartes walks into an inn. The innkeeper asks Descartes if he would like something to drink. Descartes replies, “I think not,” and promptly vanishes into thin air!

This joke can be summarized in the following argument: If I think, then I am. I think not. Therefore, I am not. 

(a) Represent this argument symbolically.

(b) Is it a valid argument?

(c) Explain your answer using either a standard form of argument or using a truth table.