Answer
The major and minor premises are represented diagrammatically. All that is known is that the Aaron dot is located somewhere outside of the dogs disk. Where it is located with respect to the carnivores disk cannot be determined. Either of the situations illustrated in the diagram (a) or (b) might be the case.
The conclusion that "Aaron is not carnivorous" is true in case (b) but not in case (a). Because the conclusion does not necessarily follow from the premises, the argument is invalid.
b. The argument form is invalid. It is the inverse error. Part (a) is a particular example of this argument form.
Work Step by Step
b. Inverse Error: $\forall x$ if $P(x)$ then $Q(x)$.
~$P(a)$ for a particular $a$.
$\therefore$ ~$Q(a)$. (invalid conclusion)
Part (a) illustrates this error: P(x) is: x is a dog. Q(x) is: x is carnivorous. a is Aaron.
~$P(a)$ is: Aaron is not a dog.
~$Q(a)$ is: Aaron is not carnivorous.
