document.write( "Question 630377: Construct a truth table for q ↔ (p^ ~q) \n" ); document.write( "

Algebra.Com's Answer #396884 by Theo(13342) $\"\"$ $\"About$

You can put this solution on YOUR website!
your truth table is shown below:
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document.write( "     p     q    ~q    (p^~q)    q <-> (p^~q)\r\n" );
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document.write( "     T     T     F      F           F\r\n" );
document.write( "     T     F     T      T           F\r\n" );
document.write( "     F     T     F      F           F\r\n" );
document.write( "     F     F     T      F           T\r\n" );
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\n" ); document.write( "you have 2 variables so there will be 2*2 = 4 rows
\n" ); document.write( "p and q have 4 possible variations.
\n" ); document.write( "they are TT TF FT FF
\n" ); document.write( "those options are shown in columns 1 and 2.
\n" ); document.write( "if q is true, then ~q is false.
\n" ); document.write( "if q is false, then ~q is true
\n" ); document.write( "that fact is shown in the third column.
\n" ); document.write( "(p^~q is true if both p and ~q are true, otherwise it is false.
\n" ); document.write( "that's shown in the fourth column.
\n" ); document.write( "q <-> (p^~q) is true if they both agree (either TT or FF).
\n" ); document.write( "Otherwise it is false.
\n" ); document.write( "<-> symbol is if and only if condition .
\n" ); document.write( "-> symbol is if then condition.
\n" ); document.write( "~ means not
\n" ); document.write( "T means true
\n" ); document.write( "F means false
\n" ); document.write( "here's a lesson written by yours truly a while ago.
\n" ); document.write( "it should still be valid.
\n" ); document.write( "http://www.algebra.com/algebra/homework/Conjunction/THEO-2011-08-19.lesson
\n" ); document.write( "i'd give you more references but i ran out of time and have to go.
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