Question 1190362: MAT 145: 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.
7) If the cheese doesn’t melt, then the nachos are ruined.
The nachos are ruined.
Therefore, the cheese didn’t melt
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website!
Let M = "The cheese melts"
Let R = "The nachos are ruined"
[(~M ⊃ R) • R] ⊃ ~M
| M | R | ~M | (~M ⊃ R) | (~M ⊃ R) • R || [(~M ⊃ R) • R] ⊃ ~M |
| T | T | F | T | T || F |
| T | F | F | T | F || T |
| F | T | T | T | T || T |
| F | F | T | F | T || T |
The last line is not TTTT, so it's not valid.
This is neither Modus Ponens nor Modus Tollens.
It is the logical fallacy of "affirming the consequent".
That's because it could be that indeed the cheese melted,
and the nachos were ruined anyway.
For instance, it could be that the tortilla chips are old,
and that's why the nachos are ruined, not necessarily
because the cheese didn't melt.
Edwin
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