document.write( "Question 479319: I need to construct a truth table. I want to know if I'm on the right track
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Algebra.Com's Answer #328426 by Edwin McCravy(20086) $\"\"$ $\"About$
You can put this solution on YOUR website!
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document.write( "p    q    ~p    ~q    q⋀~p \r\n" );
document.write( "T    T     F     F     ? \r\n" );
document.write( "T    F     F     T     ?\r\n" );
document.write( "F    T     T     F     ?\r\n" );
document.write( "F    F     T     T     ?\r\n" );
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document.write( "You need to learn the rules for the four basic \r\n" );
document.write( "symbols ⋀, ⋁, ->, and <->\r\n" );
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document.write( "Rules:\r\n" );
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document.write( "⋀ is T only for T⋀T, otherwise it's F.\r\n" );
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document.write( "⋁ is F only for F⋁F, otherwise it's T.\r\n" );
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document.write( "-> is F only for T->F, otherwise it's T.\r\n" );
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document.write( "<-> is T for T<->T, F<->F. <-> is F for T<->F, F<->T.\r\n" );
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document.write( "You only have ⋀ here to do, but you need to learn \r\n" );
document.write( "those other three rules as well for other truth tables.\r\n" );
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document.write( "Here goes:\r\n" );
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document.write( "p    q    ~p    ~q    q⋀~p \r\n" );
document.write( "T    T     F     F     ?      \r\n" );
document.write( "T    F     F     T     ?\r\n" );
document.write( "F    T     T     F     ?\r\n" );
document.write( "F    F     T     T     ?\r\n" );
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document.write( "Let's look at q⋀~p. \r\n" );
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document.write( "Let's do the top line:\r\n" );
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document.write( "On the left of the ⋀ in q⋀~p is q, and on the top line q has T under it.\r\n" );
document.write( "On the right of the ⋀ in q⋀~p is ~p, and on the top line ~p has F under it.\r\n" );
document.write( "So on the top line  q⋀~p is a case of T⋀F. So we look at the rule \r\n" );
document.write( "for ⋀, which is:\r\n" );
document.write( "\"⋀ is T only for T⋀T, otherwise it's F.\"\r\n" );
document.write( "T⋀F is not a case of T⋀T, and therefore it's F.  So we put an F\r\n" );
document.write( "on the top row underneath q⋀~p.  So we now have this:\r\n" );
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document.write( "p    q    ~p    ~q    q⋀~p \r\n" );
document.write( "T    T     F     F     F      \r\n" );
document.write( "T    F     F     T     ?\r\n" );
document.write( "F    T     T     F     ?\r\n" );
document.write( "F    F     T     T     ?\r\n" );
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document.write( "--------------------------------------------------------------  \r\n" );
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document.write( "Next let's do the second line:\r\n" );
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document.write( "On the left of the ⋀ in q⋀~p is q, and on the 2nd line q has F under it.\r\n" );
document.write( "On the right of the ⋀ in q⋀~p is ~p, and on the 2nd line ~p has F under it.\r\n" );
document.write( "So on the 2nd line  q⋀~p is a case of F⋀F. So we look at the rule \r\n" );
document.write( "for ⋀, which is:\r\n" );
document.write( "\"⋀ is T only for T⋀T, otherwise it's F.\"\r\n" );
document.write( "F⋀F is not a case of T⋀T, and therefore it's F.  So we put an F\r\n" );
document.write( "on the 2nd line underneath q⋀~p.  So we now have this:\r\n" );
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document.write( "p    q    ~p    ~q    q⋀~p \r\n" );
document.write( "T    T     F     F     F      \r\n" );
document.write( "T    F     F     T     F\r\n" );
document.write( "F    T     T     F     ?\r\n" );
document.write( "F    F     T     T     ?\r\n" );
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document.write( "--------------------------------------------------------------\r\n" );
document.write( " \r\n" );
document.write( "Next let's do the third line:\r\n" );
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document.write( "On the left of the ⋀ in q⋀~p is q, and on the 3rd line q has T under it.\r\n" );
document.write( "On the right of the ⋀ in q⋀~p is ~p, and on the 3rd line ~p has T under it.\r\n" );
document.write( "So on the 3rd line  q⋀~p is a case of T⋀T. So we look at the rule \r\n" );
document.write( "for ⋀, which is:\r\n" );
document.write( "\"⋀ is T only for T⋀T, otherwise it's F.\"\r\n" );
document.write( "T⋀T is INDEED a case of T⋀T, and therefore it's T.  So we put a T\r\n" );
document.write( "on the 3rd row underneath q⋀~p.  So we now have this:\r\n" );
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document.write( "p    q    ~p    ~q    q⋀~p \r\n" );
document.write( "T    T     F     F     F      \r\n" );
document.write( "T    F     F     T     F\r\n" );
document.write( "F    T     T     F     T\r\n" );
document.write( "F    F     T     T     ?\r\n" );
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document.write( "--------------------------------------------------------------\r\n" );
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document.write( "Next let's do the bottom line:\r\n" );
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document.write( "On the left of the ⋀ in q⋀~p is q, and on the bottom line q has F under it.\r\n" );
document.write( "On the right of the ⋀ in q⋀~p is ~p, and on the bottom line ~p has T under it.\r\n" );
document.write( "So on the bottom line q⋀~p is a case of F⋀T. So we look at the rule \r\n" );
document.write( "for ⋀, which is:\r\n" );
document.write( "\"⋀ is T only for T⋀T, otherwise it's F.\"\r\n" );
document.write( "F⋀T is not a case of T⋀T, and therefore it's F.  So we put an F\r\n" );
document.write( "on the 2nd row underneath q⋀~p.  So finally we have this:\r\n" );
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document.write( "p    q    ~p    ~q    q⋀~p \r\n" );
document.write( "T    T     F     F     F      \r\n" );
document.write( "T    F     F     T     F\r\n" );
document.write( "F    T     T     F     T\r\n" );
document.write( "F    F     T     T     F\r\n" );
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document.write( "Do you now see how truth tables are done?  You have to learn the\r\n" );
document.write( "rules for all four symbols ⋀, ⋁, ->, and <-> to do truth tables.\r\n" );
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document.write( "Edwin
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