Final answer:
The form of deductive reasoning in the given argument is a hypothetical syllogism, where the conclusion logically follows from the premises through a structure that connects conditional statements. The argument is constructed in a way that makes it valid, meaning the conclusion must be true if the premises are true.
Step-by-step explanation:
The form of deductive reasoning used in the provided argument is a hypothetical syllogism. In a hypothetical syllogism, two conditional statements are connected in a way that if the first implies the second and the second implies the third, then the first implies the third. This is shown in the steps of the argument:
- If a triangle is scalene, it has no sides of the same length.
- If a triangle has no sides of the same length, then it isn't equilateral.
- Therefore, if a triangle is scalene, then it isn't equilateral.
In summary, the argument presented takes two conditional premises and draws a conclusion that also is conditional, where the antecedent of the first premise becomes the antecedent of the conclusion, and the consequent of the second premise becomes the consequent of the conclusion.
Testing the validity of this argument involves assuming both premises are true and determining if the conclusion must also be true. Given that the structure lines up perfectly for this type of argument, it is indeed valid: it is impossible to have a scalene triangle, which by definition has no equal sides, also be equilateral, which by definition has all sides equal.