Question 1190253
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S = you are superstitious
W = you walk under a ladder
~S = you are not superstitious
~W = you do not walk under a ladder


Premise 1: S -> ~W
Premise 2: ~W -> S
Conclusion: S & ~W


Truth table:<table border = "1" cellpadding = "5"><tr><td></td><td></td><td></td><td></td><td>Premise 1</td><td>Premise 2</td><td>Conclusion</td></tr><tr><td>S</td><td>W</td><td>~S</td><td>~W</td><td>S -> ~W</td><td>~W -> ~S</td><td>S & ~W</td></tr><tr><td>T</td><td>T</td><td>F</td><td>F</td><td>F</td><td>T</td><td>F</td></tr><tr><td>T</td><td>F</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>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>T</td><td>F</td><td>F</td></tr></table>Notes:<ul><li>P -> Q is false when P is false and Q is true, otherwise it's true.</li><li>P & Q is true when both P and Q are true together, otherwise it's false</li><li>Whatever you find in column S, flip it to get ~S, and vice versa. Same goes for W to ~W as well.</li></ul>In the table above, the row marked in red highlights a case when we have all true premises but they lead to a false conclusion.
 

This directly leads to the fact <font color=red>the argument is invalid</font>.
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