Determine whether the following argument is correct. If it's not correct, explain what is wrong with ther 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.
this is a mixed hypothetical statement.
there are 4 forms, 2 are valid 2 are not.
let the antecedent of the first statement be t, and consequent be e.
~p = not p
thus we get
t } e
~e
:; ~t
This is modus tollens literally the way that denies by denying, which is a valid argument.
Sounds like a logical argument.
To determine whether the argument is correct, we need to carefully analyze the logical structure and the truth of each statement within the argument.
The given argument is a syllogism using a conditional statement. Let's break it down into its components:
Major premise: If a triangle is equilateral, then it has three equal sides.
Minor premise: Triangle ABC doesn't have three equal sides.
Conclusion: Therefore, triangle ABC isn't equilateral.
The major premise states a general rule about equilateral triangles, which is true. All equilateral triangles indeed have three equal sides.
The minor premise claims that triangle ABC does not have three equal sides. This statement might be true or false, depending on additional information about triangle ABC. Without specific information about the sides of triangle ABC, we cannot determine the validity of the argument.
If the minor premise is indeed true, then the conclusion reached is valid; triangle ABC would not be equilateral since equilateral triangles must have three equal sides.
To make the argument valid, we could change the minor premise to provide specific information about triangle ABC. For example, we could state, "Triangle ABC has two sides of equal length." With this revised minor premise, the conclusion that triangle ABC is not equilateral would be supported and logically sound.