Question 1151809
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premise1 = p v ~q
premise2 = ~q -> p
conclusion = p


p is some logical statement that can be either true (T) or false (F)
q is also either T or F
The first two columns of the table below represent the four possible ways to have a T and F combo


The third column ~q represents the negation of column q. This is the opposite of the q column.


The fourth column has p and ~q in a disjunction. A disjunction is only false when both parts are false; otherwise, it is true.


The ~q -> p column is only false when ~q is true while p is false, ie in the form T -> F; otherwise it is true.


The last column is just a copy of the first column. It's to help set up the conclusion which is often the last column.


Truth Table
<table border = "1" cellpadding = "5">
<tr><td>p</td><td>q</td><td>~q</td><td>p v ~q</td><td>~q -> p</td><td>p</td></tr>
<tr><td>T</td><td>T</td><td>F</td><td>T</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>F</td><td>T</td><td>F</td></tr>
<tr><td>F</td><td>F</td><td>T</td><td>T</td><td>F</td><td>F</td></tr>
</table>
An invalid argument would be if all the premises were true and they lead to a false conclusion. That doesn't happen here because the first two rows have a true conclusion while the last two rows have not all premises being true.


<font color=red size=4>So the argument is valid.</font>
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