document.write( "Question 483286: let p represent a true statement while q and r represent false statements. find the truth value of the compound statement
\n" ); document.write( "p^(qV~r)
\n" ); document.write( "true or false \n" ); document.write( "

Algebra.Com's Answer #330752 by Theo(13342) $\"\"$ $\"About$

You can put this solution on YOUR website!
you have three variables.
\n" ); document.write( "they are p, q, and r.
\n" ); document.write( "your compound statement is p ^ (q v ~r)
\n" ); document.write( "in english that would be:
\n" ); document.write( "p AND (q OR (not r))
\n" ); document.write( "here's your truth table:
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document.write( "           p   q   r   ~r   (q v ~r)   p ^ (q v ~r)\r\n" );
document.write( "           -   -   -   --   --------   ------------\r\n" );
document.write( "           T   T   T    F       T          T *****\r\n" );
document.write( "           T   T   F    T       T          T *****\r\n" );
document.write( "           T   F   T    F       F          F\r\n" );
document.write( "           T   F   F    T       T          T *****\r\n" );
document.write( "           F   T   T    F       T          F\r\n" );
document.write( "           F   T   F    T       T          F\r\n" );
document.write( "           F   F   T    F       F          F\r\n" );
document.write( "           F   F   F    T       T          F\r\n" );
document.write( "

\n" ); document.write( "from this table, you can see that:
\n" ); document.write( "if p is true and (q or ~r) is true, then p ^ (q v ~r) is true.
\n" ); document.write( "in all other cases, p ^ (q v ~r) is false.\r
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\n" ); document.write( "\n" ); document.write( "note that only one of q and ~r has to be true in order for the compound statement of (q v ~r) to be true.
\n" ); document.write( "if p is true, then the OR statement is true.
\n" ); document.write( "if ~q is true, then the OR statement is true.
\n" ); document.write( "The OR statement is only false if both p and q are false.\r
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