EXAMPLE 2.2.17

Select the statement that is a valid conclusion from the following premises, if a valid conclusion is warrented.

If you aren't a good stirrer, then you aren't handy with a swizzle stick.

If you are a graduate of Billy Bob's Big Bold School of Mixology, then you are a bartender.

No good stirrers have weak wrist muscles.

If you don't have weak wrist muscles, then you have a firm handshake.

All bartenders are handy with a swizzle stick.

A. If you are a graduate of Billy Bob's Big Bold School of Mixology, then you don't have a firm handshake.

B. If you don't have a firm handshake, then you aren't a graduate of Billy Bob's Big Bold School of Mixology.

C. If you have a firm handshake, then you are a graduate of Billy Bob's Big Bold School of Mixology.

D. None of these is warranted.

SOLUTION

We have this symbolic arrangement of premises:

In order to establish a chain of reasoning, we can start with the second premise. Choosing and linking premises as needed, we have this scheme:

From this we can arrive at a valid conclusion:

In words, a valid conclusion is "If you are a graduate of Billy Bob's Big Bold School of Mixology, then you have a firm handshake."

Another valid conclusion is the contrapositive of the statement written above: "If you don't have a firm handshake, then you aren't a graduate of Billy Bob's Big Bold School of Mixology."

The correct choice is B.