document.write( "Question 1181636: Find the truth value of the following: Show the solution.\r
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Algebra.Com's Answer #811553 by Edwin McCravy(20063)\"\" \"About 
You can put this solution on YOUR website!
4. (q∨r)↔[(¬q→(r∧¬p))]
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document.write( "Put TTTTFFFF under the p\r\n" );
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document.write( "Put TTFFTTFF under the q's\r\n" );
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document.write( "Put TFTFTFTF under the r's\r\n" );
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document.write( " (q∨r)↔[(¬q→(r∧¬p))]\r\n" );
document.write( "  T T     T  T  T   \r\n" );
document.write( "  T F     T  F  T  \r\n" );
document.write( "  F T     F  T  T  \r\n" );
document.write( "  F F     F  F  T  \r\n" );
document.write( "  T T     T  T  F  \r\n" );
document.write( "  T F     T  F  F  \r\n" );
document.write( "  F T     F  T  F  \r\n" );
document.write( "  F F     F  F  F \r\n" );
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document.write( "Under the two ¬'s, put the opposite of what immediately follows the ¬'s and\r\n" );
document.write( "then erase what follows them:\r\n" );
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document.write( " (q∨r)↔[(¬q→(r∧¬p))]\r\n" );
document.write( "  T T    F   T F   \r\n" );
document.write( "  T F    F   F F  \r\n" );
document.write( "  F T    T   T F  \r\n" );
document.write( "  F F    T   F F  \r\n" );
document.write( "  T T    F   T T  \r\n" );
document.write( "  T F    F   F T  \r\n" );
document.write( "  F T    T   T T  \r\n" );
document.write( "  F F    T   F T\r\n" );
document.write( "     \r\n" );
document.write( "Under the ∨ put T if there is a T immediately on either side of the ∨,\r\n" );
document.write( "and an F if there is no T on either side of the ∨. (two F's).  Then erase\r\n" );
document.write( "what was left and right of the ∨.\r\n" );
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document.write( " (q∨r)↔[(¬q→(r∧¬p))]\r\n" );
document.write( "   T     F   T F   \r\n" );
document.write( "   T     F   F F  \r\n" );
document.write( "   T     T   T F  \r\n" );
document.write( "   F     T   F F  \r\n" );
document.write( "   T     F   T T  \r\n" );
document.write( "   T     F   F T  \r\n" );
document.write( "   T     T   T T  \r\n" );
document.write( "   F     T   F T\r\n" );
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document.write( "Under the ∧ put F if there is an F immediately on either side of the ∧,\r\n" );
document.write( "and a T if there is no F on either side of the ∧ (two T's).  Then erase\r\n" );
document.write( "what was left and right of the ∧.\r\n" );
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document.write( " (q∨r)↔[(¬q→(r∧¬p))]\r\n" );
document.write( "   T     F    F   \r\n" );
document.write( "   T     F    F  \r\n" );
document.write( "   T     T    F  \r\n" );
document.write( "   F     T    F  \r\n" );
document.write( "   T     F    T  \r\n" );
document.write( "   T     F    F  \r\n" );
document.write( "   T     T    T  \r\n" );
document.write( "   F     T    F\r\n" );
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document.write( "Under the → put T unless there is a T on the left of the → and an F on\r\n" );
document.write( "the right of the →.  That's the only time you put F under →.  Then erase\r\n" );
document.write( "what is on both sides of the → \r\n" );
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document.write( " (q∨r)↔[(¬q→(r∧¬p))]\r\n" );
document.write( "   T       T     \r\n" );
document.write( "   T       T    \r\n" );
document.write( "   T       F    \r\n" );
document.write( "   F       F    \r\n" );
document.write( "   T       T    \r\n" );
document.write( "   T       T    \r\n" );
document.write( "   T       T    \r\n" );
document.write( "   F       F  \r\n" );
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document.write( "Finally, put T under ↔ if what are on both sides of ↔ are alike,\r\n" );
document.write( "either both T's or both F's, and put F under ↔ if they are different.\r\n" );
document.write( "Then erase what is on both sides of the ↔\r\n" );
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document.write( " (q∨r)↔[(¬q→(r∧¬p))]\r\n" );
document.write( "      T          \r\n" );
document.write( "      T         \r\n" );
document.write( "      F         \r\n" );
document.write( "      T         \r\n" );
document.write( "      T         \r\n" );
document.write( "      T          \r\n" );
document.write( "      T          \r\n" );
document.write( "      T     \r\n" );
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document.write( "The answer is TTFTTTTT.\r\n" );
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document.write( "---------------\r\n" );
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5. (¬s↔(r→¬q))↔[(s∨p)∧¬(q∧r)]
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document.write( "That will take 16 lines.  I'll start it off. You finish using the same rules\r\n" );
document.write( "as above.\r\n" );
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document.write( "Put TTTTTTTTFFFFFFFF under the p.\r\n" );
document.write( "Put TTTTFFFFTTTTFFFF under the q's.\r\n" );
document.write( "Put TTFFTTFFTTFFTTFF under the r's.\r\n" );
document.write( "Put TFTFTFTFTFTFTFTF under the s's.\r\n" );
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document.write( "(¬s↔(r→¬q))↔[(s∨p)∧¬(q∧r)]\r\n" );
document.write( "  T  T  T     T T    T T\r\n" );
document.write( "  F  T  T     F T    T T\r\n" );
document.write( "  T  F  T     T T    T F\r\n" );
document.write( "  F  F  T     F T    T F\r\n" );
document.write( "  T  T  F     T T    F T\r\n" );
document.write( "  F  T  F     F T    F T\r\n" );
document.write( "  T  F  F     T T    F F\r\n" );
document.write( "  F  F  F     F T    F F\r\n" );
document.write( "  T  T  T     T F    T T\r\n" );
document.write( "  F  T  T     F F    T F\r\n" );
document.write( "  T  F  T     T F    T F\r\n" );
document.write( "  F  F  T     F F    T T\r\n" );
document.write( "  T  T  F     T F    F T\r\n" );
document.write( "  F  T  F     F F    F T\r\n" );
document.write( "  T  F  F     T F    F T\r\n" );
document.write( "  F  F  F     F F    F T   \r\n" );
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document.write( "Edwin
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