Question 1190422
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Another way to form the truth table is to write it like this<table border = "1" cellpadding = "5"><tr><td></td><td></td><td></td><td>Premise 1</td><td>Premise 2</td><td>Conclusion</td></tr><tr><td>P</td><td>Q</td><td>~Q</td><td>P -> ~Q</td><td>P v Q</td><td>P</td></tr><tr><td>T</td><td>T</td><td>F</td><td>F</td><td>T</td><td>T</td></tr><tr><td>T</td><td>F</td><td>T</td><td>T</td><td>T</td><td>T</td></tr><tr><td>F</td><td>T</td><td>F</td><td><font color=red>T</font></td><td><font color=red>T</font></td><td><font color=red>F</font></td></tr><tr><td>F</td><td>F</td><td>T</td><td>T</td><td>F</td><td>F</td></tr></table>The row marked in red has all true premises but a false conclusion.


Therefore, the argument is <font color=red size=4>invalid</font>.


Side notes:<ul><li>The row I marked in red is the same row number that Edwin had F in the last column of the table (ie it corresponds to the same P = F and Q = T values).</li><li>P v Q is false only when both P and Q are false together; otherwise, it's true.</li><li>P -> Q is false only when a true antecedent (P) leads to a false conclusion (Q). It's effectively how both variations of proof invalidations are done. </li><li>Stuff in the ~Q column is the flip of what is found in the Q column</li></ul>
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