Final answer:
If a Euler diagram allows a conclusion that doesn't follow from its premises, the argument is invalid because it does not guarantee the truth of the conclusion if the premises are true.
Step-by-step explanation:
If a Euler diagram can be drawn in a way in which the conclusion does not necessarily follow from the premises, the syllogistic argument is an invalid argument. This means that although the premises might be true, they do not logically guarantee the conclusion's truth. Validity is a feature of the argument's form and does not depend on the truth of the premises or conclusion but on the logical connection between them. For an argument to be valid, if the premises are true, the conclusion must also be necessarily true.
Examples of Valid Deductive Inferences:
- Disjunctive Syllogism
- Modus Ponens
- Modus Tollens
Common Problems with Invalid Arguments:
- Premises are false or questionable
- Premises are irrelevant
- Premises are inadequate to support the conclusion
- Alternative arguments exist with equal or greater support