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.