document.write( "Question 147603: Can someone help me construct this truth table? P->(P ->(Q ^ P)). Now, does this mean that first, you work the Q^P? or do you work the p-> which is inside the ( ) first. Then do you take the result of whichever is used and connect it with p-> which is oustide the ( ). Do that make sense. I'm confused too. \n" ); document.write( "
Algebra.Com's Answer #107986 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
Can someone help me construct this truth table? P->(P ->(Q ^ P)). Now, does this mean that first, you work the Q^P? or do you work the p-> which is inside the ( ) first. Then do you take the result of whichever is used and connect it with p-> which is oustide the ( ). Do that make sense. I'm confused too.
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document.write( "Start with this:\r\n" );
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document.write( "P|Q| P->(P ->(Q ^ P))\r\n" );
document.write( "T|T|   \r\n" );
document.write( "T|F|    \r\n" );
document.write( "F|T|  \r\n" );
document.write( "F|F| \r\n" );
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document.write( "Now transfer TTFF under every P, and TFTF under every Q\r\n" );
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document.write( "P|Q| P->(P ->(Q ^ P))\r\n" );
document.write( "T|T| T   T    T   T  \r\n" );
document.write( "T|F| T   T    F   T   \r\n" );
document.write( "F|T| F   F    T   F  \r\n" );
document.write( "F|F| F   F    F   F\r\n" );
document.write( "\r\n" );
document.write( "Now take care of the ^, because that's the innermost\r\n" );
document.write( "operation.  If ^ is between two T's it's T, otherwise it's F\r\n" );
document.write( "So we use this rule to fill in under the ^, but everytime\r\n" );
document.write( "we do we scratch through the letters on each side of it,\r\n" );
document.write( "like this:\r\n" );
document.write( "\r\n" );
document.write( "P|Q| P->(P ->(Q ^ P))\r\n" );
document.write( "T|T| T   T    T T T  \r\n" );
document.write( "T|F| T   T    F F T   \r\n" );
document.write( "F|T| F   F    T F F  \r\n" );
document.write( "F|F| F   F    F F F\r\n" );
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document.write( "Now I'll just erase them, but you can just leave them\r\n" );
document.write( "scratched:\r\n" );
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document.write( "P|Q| P->(P ->(Q ^ P))\r\n" );
document.write( "T|T| T   T      T    \r\n" );
document.write( "T|F| T   T      F     \r\n" );
document.write( "F|T| F   F      F    \r\n" );
document.write( "F|F| F   F      F\r\n" );
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document.write( "Now take care of the second ->, because that's now the innermost\r\n" );
document.write( "operation.  If -> has a T on the left and an F on the right,\r\n" );
document.write( "then it's F, otherwise it's T. So we use this rule to fill \r\n" );
document.write( "in under the ->, but as before, every time we do we scratch \r\n" );
document.write( "through the letters on each side of it, like this:  \r\n" );
document.write( "\r\n" );
document.write( "P|Q| P->(P ->(Q ^ P))\r\n" );
document.write( "T|T| T   T  T   T    \r\n" );
document.write( "T|F| T   T  F   F     \r\n" );
document.write( "F|T| F   F  T   F    \r\n" );
document.write( "F|F| F   F  T   F\r\n" );
document.write( "\r\n" );
document.write( "Again I'll erase the ones scratched, but you can just leave them\r\n" );
document.write( "scratched:\r\n" );
document.write( "\r\n" );
document.write( "P|Q| P->(P ->(Q ^ P))\r\n" );
document.write( "T|T| T      T       \r\n" );
document.write( "T|F| T      F        \r\n" );
document.write( "F|T| F      T       \r\n" );
document.write( "F|F| F      T   \r\n" );
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document.write( "Finally we take care of the first ->, because that's now \r\n" );
document.write( "the innermost operation.  We use the same rule again to fill \r\n" );
document.write( "in under the first ->,\r\n" );
document.write( "\r\n" );
document.write( "P|Q| P->(P ->(Q ^ P))\r\n" );
document.write( "T|T| T T    T       \r\n" );
document.write( "T|F| T F    F        \r\n" );
document.write( "F|T| F T    T       \r\n" );
document.write( "F|F| F T    T   \r\n" );
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document.write( "And erasing those marked thru:\r\n" );
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document.write( "P|Q| P->(P ->(Q ^ P))\r\n" );
document.write( "T|T|   T           \r\n" );
document.write( "T|F|   F            \r\n" );
document.write( "F|T|   T           \r\n" );
document.write( "F|F|   T     \r\n" );
document.write( "\r\n" );
document.write( "Edwin

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