document.write( "Question 1181632: Find the truth value of the following: Show the solution.\r
\n" ); document.write( "\n" ); document.write( "1. (p∨r)→[(q↔s)∧p]\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #849988 by CPhill(1959)\"\" \"About 
You can put this solution on YOUR website!
Let's determine the truth value of (p∨r)→[(q↔s)∧p] using a truth table. Since there are four variables (p, q, r, s), there are 2⁴ = 16 possible combinations of truth values.\r
\n" ); document.write( "\n" ); document.write( "Here's the truth table:\r
\n" ); document.write( "\n" ); document.write( "| p | q | r | s | p∨r | q↔s | (q↔s)∧p | (p∨r)→[(q↔s)∧p] |
\n" ); document.write( "|---|---|---|---|-----|-----|--------|-----------------|
\n" ); document.write( "| T | T | T | T | T | T | T | T |
\n" ); document.write( "| T | T | T | F | T | F | F | F |
\n" ); document.write( "| T | T | F | T | T | T | T | T |
\n" ); document.write( "| T | T | F | F | T | F | F | F |
\n" ); document.write( "| T | F | T | T | T | F | F | F |
\n" ); document.write( "| T | F | T | F | T | T | T | T |
\n" ); document.write( "| T | F | F | T | T | F | F | F |
\n" ); document.write( "| T | F | F | F | T | T | T | T |
\n" ); document.write( "| F | T | T | T | T | T | F | F |
\n" ); document.write( "| F | T | T | F | T | F | F | F |
\n" ); document.write( "| F | T | F | T | F | T | F | T |
\n" ); document.write( "| F | T | F | F | F | F | F | T |
\n" ); document.write( "| F | F | T | T | T | F | F | F |
\n" ); document.write( "| F | F | T | F | T | T | F | F |
\n" ); document.write( "| F | F | F | T | F | F | F | T |
\n" ); document.write( "| F | F | F | F | F | T | F | T |\r
\n" ); document.write( "\n" ); document.write( "Since the final column has both T and F values, the given statement is a **contingency**. Its truth value depends on the specific truth values of p, q, r, and s.
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