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:

1. not good stirrer arrow not handy.

2. graduate arrow bartender.

3. good stirrer arrow not weak wrist.

4. not weak wrist arrow firm handshake.

5. bartender arrow handy.

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:

2. graduate arrow bartender.

5. bartender arrow handy.

1. handy arrow good stirrer.

3. good stirrer arrow weak wrist.

4. not weak wrist arrow firm handshake.

From this we can arrive at a valid conclusion:

Graduate arrow firm handshake.

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.