Question

Determine if it's the law of detachment, syllogism, or invalid.

(1) If a triangle is equilateral, then it is equiangular.
(2) If a triangle is equiangular, then none of its angles are obtuse.
(3) If a triangle is equilateral, then none of its angles are obtuse.
A) Option A: Law of Detachment
B) Option B: Syllogism
C) Option C: Invalid
D) Option D: None of the above

Answer 1

The statements given lead to a logical conclusion through a common term, thus forming a syllogism, which is a type of deductive reasoning aimed at arriving at a valid conclusion from two related premises.

Step-by-step explanation:

The given statements form a logical sequence that can be identified as a syllogism. A syllogism is a form of deductive reasoning where a conclusion is drawn from two given or assumed propositions (premises), each of which shares a common or middle term not present in the conclusion.

In this case:

1. If a triangle is equilateral, then it is equiangular.
2. If a triangle is equiangular, then none of its angles are obtuse.
3. Therefore, if a triangle is equilateral, then none of its angles are obtuse.

These statements demonstrate that they share a common term ('equiangular'), which leads to a logical conclusion that an equilateral triangle cannot have obtuse angles. This logical progression is a classic example of a syllogism. It is important to discern such logical structures to strengthen deductive reasoning skills and ensure the validity of conclusions in mathematical proofs and arguments.