SOLUTION: MAT 145: Topics In Contemporary Math QUESTION 9 Translate the argument into symbols. Identify which argument for it uses. Determine if the argument is valid or invalid.

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Question 1190424: MAT 145: Topics In Contemporary Math


QUESTION 9
Translate the argument into symbols. Identify which argument for it uses. Determine if the argument is valid or invalid.
If Adora is a princess, then she fights the Horde.
Adora does not fight the Horde.
Therefore, Adora is not a princess.
Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

T = true
F = false

P = Adora is a princess
H = she (Adora) fights the horde

~P = Adora is not a princess
~H = she does not fight the horde

Premise 1: P -> H
Premise 2: ~H
Conclusion: ~P

The arrow notation P -> Q means "If P, then Q".

Here's what the truth table looks like
Premise 1Premise 2Conclusion
PHP -> H~H~P
TTTFF
TFFTF
FTTFT
FFTTT

P -> H is only true when P is true while H is false. Otherwise, the conditional statement is true.
~H will flip everything in the H column.
~P flips everything in the P column.

As the table shows, we do not have any rows with all true premises lead to a false conclusion.
This means we are not able to prove the argument is invalid.
Therefore, this argument is valid.

The argument is valid by the modus tollens rule.

---------------------------------------------------------

Here's another way to form the truth table and to show we have a valid argument
PHP -> H~H(P -> H) & ~H[ (P -> H) & ~H ] -> ~P
TTTFFT
TFFTFT
FTTFFT
FFTTTT
The last column is all T, so there are no cases in which the argument is invalid.
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