Question 1190301
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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 <font color=red>valid by disjunctive syllogism</font>.


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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 <font color=red>modus ponens</font> to go from ~C -> S to S


In other words, this argument below
Premise 1: ~C -> S
Premise 2: ~C
Conclusion: S
uses <font color=red>modus ponens</font>


Meanwhile, this argument
Premise 1: ~S -> C
Premise 2: ~C
Conclusion: S
uses <font color=red>modus tollens</font>


So there are a few ways to show that this argument is valid.
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