Question 1190299
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The law of disjunctive syllogism has an argument of this format
Premise 1: P v Q
Premise 2: ~P
Conclusion: Q


Truth table:<table border = "1" cellpadding = "5"><tr><td></td><td></td><td>Premise 1</td><td>Premise 2</td><td>Conclusion</td></tr><tr><td>P</td><td>Q</td><td>P v Q</td><td>~P</td><td>Q</td></tr><tr><td>T</td><td>T</td><td>T</td><td>F</td><td>T</td></tr><tr><td>T</td><td>F</td><td>T</td><td>F</td><td>F</td></tr><tr><td>F</td><td>T</td><td>T</td><td>T</td><td>T</td></tr><tr><td>F</td><td>F</td><td>F</td><td>T</td><td>F</td></tr></table>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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