# Invalidity and truth

Mr. Nance,

I have a question on Intermediate Logic, Test 2, Form B, Problem 4. The question says: “An invalid argument can have true premises and a true conclusion, is this true or false?” The answer book says it’s true but the definition of an invalid argument would prove that statement to be false. Is there a typo or is that correct?

No, this is correct. You may be thinking that in an invalid argument, the premises can be true and the conclusion false. But note that this does not say that in an invalid argument the premises are necessarily true and the conclusion false.

Here is an example of an invalid argument, with true premises and a false conclusion:

All dogs are mammals.
All cats are mammals.
Therefore, all cats are dogs.

The true premises and false conclusion demonstrate that it is invalid. But this very similar invalid argument has true premises and a true conclusion:

All dogs are mammals.
All poodle are mammals.
Therefore, all poodles are dogs.

The premises here still do not imply the conclusion. This argument is invalid, and in fact has an identical form as the first (AAA-2). But every statement in this second argument is true.

Hence, an invalid argument can have true premises and a true conclusion.