Question

Which statement is true about this argument?


Premises:

If a triangle has three sides of equal length, then it is an equilateral triangle.

The side lengths of △DEF


are 3 cm, 3 cm, and 3 cm.


Conclusion:

△DEF


is an equilateral triangle.


A.) The argument is not valid because the conclusion does not follow from the premises.

B.) The argument is valid by the law of syllogism.

C.) The argument is valid by the law of detachment.

D.) The argument is not valid because the premises are not true.

Answer 1

Answer:

The argument is valid by the law of detachment.

Step-by-step explanation:

The law states exactly that, if p implies q and p is true, then you can deduce q. In this case, you know that having three equal sides makes you equilateral. You have three equal sides, so you are equilateral.

Answer 2

There are several laws that can be used to prove mathematical statements.

For the given parameters, the true statement is (C) The argument is valid by the law of detachment.

The given parameter implies that:

All triangles with equal side lengths are equilateral triangle

The law of detachment states that: If p implies q, then q is true, if p is true

This means that:

If the side lengths of △DEF  are equal (i.e. 3 cm)

Then

△DEF is an equilateral triangle

Hence, the argument is valid and the true option is: (C)

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