Problem 1: Consider the statement "No good vegetables are yellow", and rewrite in in the form x ,if P ( x ) then Q ( x ), explicitly specifying the meaning of P ( x ) and Q ( x ). Using this, determine if the following argument is valid or invalid and explain why:

No good vegetables are yellow.

Wax beans are yellow.

Therefore, wax beans are not good.

Problem 2: Indicate whether the below argument is valid or invalid, and draw a diagram representing the argument. If it is valid and corresponds to a standard argument form, name that argument form.

All rational functions are differentiable on their domains.

All functions differentiable on their domains are continuous on their domains.

Therefore, all rational functions are continuous on their domains.

Problem 3: Prove that for any odd integers a and b, a 2 + b is even.