document.write( "Question 1181634: Find the truth value of the following: Show the solution.\r
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\n" ); document.write( "3. [(q∨¬p)↔(r→p)]→(q∨s)
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Algebra.Com's Answer #849986 by CPhill(1959)\"\" \"About 
You can put this solution on YOUR website!
Let's determine the truth value of the statement [(q∨¬p)↔(r→p)]→(q∨s) 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 | q∨¬p | r→p | (q∨¬p)↔(r→p) | q∨s | [(q∨¬p)↔(r→p)]→(q∨s) |
\n" ); document.write( "|---|---|---|---|----|------|-----|----------------|-----|--------------------------|
\n" ); document.write( "| T | T | T | T | F | T | T | T | T | T |
\n" ); document.write( "| T | T | T | F | F | T | T | T | T | T |
\n" ); document.write( "| T | T | F | T | F | T | T | T | T | T |
\n" ); document.write( "| T | T | F | F | F | T | T | T | T | T |
\n" ); document.write( "| T | F | T | T | F | F | T | F | T | T |
\n" ); document.write( "| T | F | T | F | F | F | T | F | F | T |
\n" ); document.write( "| T | F | F | T | F | F | T | F | T | T |
\n" ); document.write( "| T | F | F | F | F | F | T | F | F | T |
\n" ); document.write( "| F | T | T | T | T | T | F | F | T | T |
\n" ); document.write( "| F | T | T | F | T | T | F | F | T | T |
\n" ); document.write( "| F | T | F | T | T | T | T | T | T | T |
\n" ); document.write( "| F | T | F | F | T | T | T | T | T | T |
\n" ); document.write( "| F | F | T | T | T | T | F | F | T | T |
\n" ); document.write( "| F | F | T | F | T | T | F | F | F | T |
\n" ); document.write( "| F | F | F | T | T | T | T | T | T | T |
\n" ); document.write( "| F | F | F | F | T | T | T | T | F | F |\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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