Question 1190470
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T = true
F = false


Here are some facts to memorize<ul><li>p v q is false when both p and q are false together; otherwise it's true</li><li>p ^ q is true when both p and q are true together; otherwise, it's false</li><li>p -> q is false when p is true and q is false; otherwise it's true</li><li>~p is the opposite of column p (i.e. flip everything in column p)</li></ul>With all that in mind, we have this truth table<table border = "1" cellpadding = "5"><tr><td>p</td><td>q</td><td>r</td><td>~p</td><td>p -> q</td><td>r v ~p</td><td>(p -> q) ^ (r v ~p)</td></tr><tr><td>T</td><td>T</td><td>T</td><td>F</td><td>T</td><td>T</td><td>T</td></tr><tr><td>T</td><td>T</td><td>F</td><td>F</td><td>T</td><td>F</td><td>F</td></tr><tr><td>T</td><td>F</td><td>T</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>F</td><td>F</td><td>F</td><td>F</td></tr><tr><td>F</td><td>T</td><td>T</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>T</td><td>T</td><td>T</td><td>T</td></tr><tr><td>F</td><td>F</td><td>T</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>T</td><td>T</td><td>T</td></tr></table>
Notice we need 8 rows because of the 3 variables (p,q,r).
2^3 = 8


Column p has four T's in a row, followed by four F's in a row.
Column q has two copies of TTFF
Column r has four copies of TF
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