document.write( "Question 1171518: For any TFL sentences 𝛼, 𝛽, and 𝛾 such that 𝛼 is a contradiction, 𝛽 is a tautology, and 𝛾 is neither a contradiction nor a tautology, do the following entailments hold:\r
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Algebra.Com's Answer #797641 by Edwin McCravy(20055)\"\" \"About 
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document.write( "𝛼 β†’ 𝛼 ⊨ 𝛽 β†’ (𝛽 β†’ 𝛼)\r\n" );
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document.write( "Substitute FALSITY for 𝛼, TRUTH for 𝛽, \r\n" );
document.write( "𝛼 β†’ 𝛼 ⊨ 𝛽 β†’ (𝛽 β†’ 𝛼)\r\n" );
document.write( "FALSITY β†’ FALSITY ⊨ TRUTH β†’ (TRUTH β†’ FALSITY)\r\n" );
document.write( "            TRUTH ⊨ TRUTH β†’ FALSITY\r\n" );
document.write( "            TRUTH ⊨ FALSITY\r\n" );
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document.write( "Does not hold.   \r\n" );
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document.write( "3.2.2. Β¬(𝛽 β†’ 𝛾) ⊨ 𝛾 ↔ 𝛼\r\n" );
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document.write( "Substitute FALSITY for 𝛼, TRUTH for 𝛽, and leave 𝛾 as it is,\r\n" );
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document.write( "    Β¬(TRUTH β†’ 𝛾) ⊨ 𝛾 ↔ FALSITY\r\n" );
document.write( "  Β¬(Β¬TRUTH or 𝛾) ⊨ 𝛾 ↔ FALSITY\r\n" );
document.write( " Β¬(FALSITY or 𝛾) ⊨ 𝛾 ↔ FALSITY\r\n" );
document.write( " (Β¬FALSITY & ¬𝛾) ⊨ 𝛾 ↔ FALSITY\r\n" );
document.write( "    (TRUTH & ¬𝛾) ⊨ 𝛾 ↔ FALSITY\r\n" );
document.write( "              ¬𝛾 ⊨ 𝛾 ↔ FALSITY\r\n" );
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document.write( "Since the left side becomes ¬𝛾, then 𝛾 would have to be a falsity and\r\n" );
document.write( "would imply falsity. \r\n" );
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document.write( "Yes, it does hold.\r\n" );
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document.write( "Edwin
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