Final answer:
A geometrical proof is based on deductive reasoning, which guarantees the conclusion's truth if the premises are true. This statement is false when it suggests that a geometrical proof is inductive, as inductive reasoning is about probability and generalization, unlike the certainty provided by deduction.
Step-by-step explanation:
A geometrical proof is an example of a deductive argument, not an inductive one. This means a geometrical proof is false when it is claimed to be inductive. In deductive reasoning, if the premises are true, the conclusion must also be true. A valid deductive inference ensures the truth of the conclusion when the premises are assumed true. In contrast, inductive reasoning involves making generalizations based on observations and is probabilistic rather than certain.
For example, a disjunctive syllogism is a structure used in deductive reasoning:
- X or Y.
- Not Y.
- Therefore X.
To test the validity of a deductive argument, one might use counterexamples to determine whether an argument is invalid - when the premises are true but the conclusion is false.