1. Are the following arguments valid? Explain. State the type of valid argument form or error that occurs.

(a) If at least one of these two numbers is divisible by 5, then the product of these two numbers is divisible by 5.

The product of these two numbers is divisible by 5.

Therefore, at least one of these two numbers is divisible by 5.

(b) If |a_n| converges, then a_n converges.

The sum b_n diverges.

Then, the sum |b_n| diverges.

2. Consider the following sequence of events.

If it is a cold evening or it is February 1, then I will stay inside.

I will not stay inside.

Can we deduce from this argument that it is not February 1? Do the following: (a) translate the sequence of events into symbols and (b) obtain the conclusion from formal logical equivalence and rules of inference.