Determine whether the following argument is correct. If it’s not correct, explain what is wrong with the argument and change the minor premise to make a correct argument.

If a triangle is equilateral, then it has three equal sides.
Triangle ABC doesn’t have three equal sides.
Therefore, triangle ABC isn’t equilateral.

Right!

To determine the correctness of the argument, we need to evaluate its logical structure.

The argument follows a standard form known as a deductive argument, which consists of a major premise, a minor premise, and a conclusion. In this case, the major premise is "If a triangle is equilateral, then it has three equal sides," the minor premise is "Triangle ABC doesn't have three equal sides," and the conclusion is "Therefore, triangle ABC isn't equilateral."

The argument is valid because it follows the structure of a valid logical form called modus tollens. Modus tollens states that if a conditional statement (if A, then B) is true, and the consequent (B) is false, then the antecedent (A) must also be false.

In this case, the major premise establishes the logical relationship between an equilateral triangle and having three equal sides. The minor premise presents the specific case of triangle ABC not having three equal sides. From this, we can conclude that triangle ABC is not equilateral.

Therefore, the argument is correct as it stands.

If we were to change the minor premise to "Triangle ABC has three equal sides," the conclusion would be incorrect because an equilateral triangle is specifically defined by having three equal sides. So, the argument would be invalid in that case.