Mr. Nance,

One of my students came up with a counter-example for OAO-1 (#6 Quiz 9) in class yesterday:

Some fish are not cats.
All catfish are fish.
∴ Some catfish are not cats.

Because of subimplication “NO catfish are cats” is true, would this counterexample be incorrect since “some catfish are not cats” is implied to be true as well? We had several class examples so by the end of the class, we were all a bit bogged down.

Thanks for your help!

This counterexample is indeed incorrect for the reason you give: the conclusion “Some catfish are not cats” is true. The form is good, and the premises are true; it just needs a false conclusion. You could get this by substituting “cats” with “creatures whose name starts ‘cat'”! That would give you this working counterexample:

Some fish are not creatures whose name starts ‘cat’.
All catfish are fish.
∴ Some catfish are not creatures whose name starts ‘cat’.

Blessings!