Question 1190301: Topics In Contemporary Math
Modus Ponens and Modus Tollens
Translate each of the following into symbols, then determine whether or not the argument
is valid by providing the appropriate name for the argument form.
3) I studied or I failed the class.
I did not fail the class.
Therefore, I studied.
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
S = I studied
C = I failed the class
It's tempting to use F to represent "I failed the class", but F has a special meaning in logic and it stands for "false". So that's why I avoided using F.
Premise 1: S v C
Premise 2: ~C
Conclusion: S
This argument is valid by disjunctive syllogism.
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If you wanted, you can rewrite premise 1 into ~S -> C which is equivalent to ~C -> S
From here, you can use modus ponens to go from ~C -> S to S
In other words, this argument below
Premise 1: ~C -> S
Premise 2: ~C
Conclusion: S
uses modus ponens
Meanwhile, this argument
Premise 1: ~S -> C
Premise 2: ~C
Conclusion: S
uses modus tollens
So there are a few ways to show that this argument is valid.
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