document.write( "Question 975439: INSTRUCTIONS: Use indirect truth tables to answer the following problems.\r
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\n" ); document.write( "Premises: (K • ∼C) ⊃ ∼(P • R)/ J ⊃ (K • P)/ A ⊃ (P • R) Conclusion: (A • J) ⊃ C\r
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\n" ); document.write( "Cogent.
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\n" ); document.write( "Sound.
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\n" ); document.write( "Valid.
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\n" ); document.write( "Uncogent.
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\n" ); document.write( "Invalid.
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Algebra.Com's Answer #597210 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "(K • ∼C) ⊃ ∼(P • R)/ J ⊃ (K • P)/ A ⊃ (P • R) Conclusion: (A • J) ⊃ C \r\n" );
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document.write( "Start the indirect truth table by putting an F under the ⊃ in the conclusion.\r\n" );
document.write( "We are assuming that the conclusion is false. If we can now show that this makes\r\n" );
document.write( "one of the premises false, then we will have shown that the assumption that the\r\n" );
document.write( "conclusion was false was a bad assumption.  Thus the conclusion will be true,\r\n" );
document.write( "and the argument valid.\r\n" );
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document.write( "(K • ∼C) ⊃ ∼(P • R)/ J ⊃ (K • P)/ A ⊃ (P • R) Conclusion: (A • J) ⊃ C \r\n" );
document.write( "                                                                    F\r\n" );
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document.write( "The only way that can be false is for (A • J) to be true and C false, so put a T\r\n" );
document.write( "under the • and F under the C\r\n" );
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document.write( "(K • ∼C) ⊃ ∼(P • R)/ J ⊃ (K • P)/ A ⊃ (P • R) Conclusion: (A • J) ⊃ C \r\n" );
document.write( "                                                               T    F F\r\n" );
document.write( "No you can put F's under all the C's\r\n" );
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document.write( "(K • ∼C) ⊃ ∼(P • R)/ J ⊃ (K • P)/ A ⊃ (P • R) Conclusion: (A • J) ⊃ C \r\n" );
document.write( "      F                                                        T    F F\r\n" );
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document.write( "Since C s false, ~C is true so put a T under the ~ of ~C\r\n" );
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document.write( "(K • ∼C) ⊃ ∼(P • R)/ J ⊃ (K • P)/ A ⊃ (P • R) Conclusion: (A • J) ⊃ C \r\n" );
document.write( "     TF                                                        T    F F\r\n" );
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document.write( "The only way (A • J) can be true is for both A and J to be true, so put\r\n" );
document.write( "T's under all the A's and J's:\r\n" );
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document.write( "(K • ∼C) ⊃ ∼(P • R)/ J ⊃ (K • P)/ A ⊃ (P • R) Conclusion: (A • J) ⊃ C \r\n" );
document.write( "     TF               T            T                         T T T  F F\r\n" );
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document.write( "Since A is true, the only way A ⊃ (P • R) can be true is for (P • R) to be \r\n" );
document.write( "true, so put a T under the • of (P • R)\r\n" );
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document.write( "(K • ∼C) ⊃ ∼(P • R)/ J ⊃ (K • P)/ A ⊃ (P • R) Conclusion: (A • J) ⊃ C \r\n" );
document.write( "     TF               T            T       T                 T T T  F F\r\n" );
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document.write( "The only way (P • R) can be true is for both P and R to be true, so put\r\n" );
document.write( "T's under all the P's and R's:\r\n" );
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document.write( "(K • ∼C) ⊃ ∼(P • R)/ J ⊃ (K • P)/ A ⊃ (P • R) Conclusion: (A • J) ⊃ C \r\n" );
document.write( "     TF       T   T   T         T   T    T T T               T T T  F F\r\n" );
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document.write( "Since J is true, the only way J ⊃ (K • P) can be true is for (K • P) to be \r\n" );
document.write( "true, so put a T under the • of (K • P)\r\n" );
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document.write( "(K • ∼C) ⊃ ∼(P • R)/ J ⊃ (K • P)/ A ⊃ (P • R) Conclusion: (A • J) ⊃ C \r\n" );
document.write( "     TF       T   T   T       T T   T    T T T               T T T  F F\r\n" );
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document.write( "The only way (K • P) can be true is for K to be true, so put T under\r\n" );
document.write( "all the K's\r\n" );
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document.write( "(K • ∼C) ⊃ ∼(P • R)/ J ⊃ (K • P)/ A ⊃ (P • R) Conclusion: (A • J) ⊃ C \r\n" );
document.write( " T   TF       T   T   T     T T T   T    T T T               T T T  F F\r\n" );
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document.write( "Since P, R are both true put a T under the • of (P • R)\r\n" );
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document.write( "(K • ∼C) ⊃ ∼(P • R)/ J ⊃ (K • P)/ A ⊃ (P • R) Conclusion: (A • J) ⊃ C \r\n" );
document.write( " T   TF       T T T   T     T T T   T    T T T               T T T  F F\r\n" );
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document.write( "Since (P • R) is true, ~(P • R) id false, so put an F under the ~\r\n" );
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document.write( "(K • ∼C) ⊃ ∼(P • R)/ J ⊃ (K • P)/ A ⊃ (P • R) Conclusion: (A • J) ⊃ C \r\n" );
document.write( " T   TF     F T T T   T     T T T   T    T T T               T T T  F F\r\n" );
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document.write( "(K • ∼C) is true becatuse K and ~C are true, so put a T under the • of\r\n" );
document.write( "(K • ∼C).\r\n" );
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document.write( "(K • ∼C) ⊃ ∼(P • R)/ J ⊃ (K • P)/ A ⊃ (P • R) Conclusion: (A • J) ⊃ C \r\n" );
document.write( " T T TF     F T T T   T     T T T   T    T T T               T T T  F F\r\n" );
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document.write( "We have reached a contradiction because (K • ∼C) ⊃ ∼(P • R) is given\r\n" );
document.write( "as a premise yet (K • ∼C) is true and ∼(P • R) is false.\r\n" );
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document.write( "Therefore since the assumption that the conclusion is false leads to a\r\n" );
document.write( "false premise, then the argument is valid.\r\n" );
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document.write( "Edwin
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