Question 1190299: Topics In Contemporary Math
Modus Ponens and Modus Tollens
1) Create a truth table to prove that the Law of Disjunctive Syllogism is a valid argument
form.
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
The law of disjunctive syllogism has an argument of this format
Premise 1: P v Q
Premise 2: ~P
Conclusion: Q
Truth table:
| | Premise 1 | Premise 2 | Conclusion | | P | Q | P v Q | ~P | Q | | T | T | T | F | T | | T | F | T | F | F | | F | T | T | T | T | | F | F | F | T | F |
Carefully look through each row.
Ask yourself: "For any single row, do I have all true premises but they lead to a false conclusion?"
The answer is "no" because row 3 comes close, but the true premises lead to a true conclusion.
Since we don't have all true premises that don't lead to a false conclusion, this means we can't prove the argument is invalid.
Therefore, the disjunctive syllogism is valid.
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An example of disjunctive syllogism:
Premise 1: I either ate pizza or I ate Quiznos
Premise 2: I didn't eat pizza
Conclusion: I ate Quiznos
Replace "I ate pizza" with P, and "I ate Quiznos" with Q to get the argument format mentioned earlier.
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