document.write( "Question 1201495: For each of the following lists of premises, derive the indicated conclusion and complete the justification. In problems 4 and 8 you can add any statement you choose. \r
\n" ); document.write( "\n" ); document.write( "(1) 1. S ∨ H 2. B • E 3. R ⊃ G 4. _____ ____, Simp
\n" ); document.write( "(2) 1. (N ⊃ T) • (F ⊃ Q) 2. (N ⊃ R) ∨ (F ⊃ M) 3. N ∨ F 4. _______________ ____, CD
\n" ); document.write( "(3) 1. D 2. W 3. ____ ____, Conj
\n" ); document.write( "(4) 1. H 2. ____ ____, Add
\n" ); document.write( "(5) 1. R • (N ∨ K) 2. (G • T) ∨ S 3. (Q • C) ⊃ (J • L) 4. _____________ ____, Simp
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Algebra.Com's Answer #835922 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "I'll just do the first 2\r\n" );
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document.write( "\"Simp\" = simplification means (p • q) ⊃ p and if you can skip\r\n" );
document.write( "\"commutation\", then (p • q) ⊃ q, also.\r\n" );
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document.write( "Think of ⊃ as the same as the word \"guarantees\".\r\n" );
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document.write( "\"Simp\" says if you have the 1st and the 2nd, then that guarantees that you have\r\n" );
document.write( "the 1st ---\r\n" );
document.write( "PLUS ---\r\n" );
document.write( "if you can skip commutation, (swapping p with q), then it also guarantees that\r\n" );
document.write( "you have the 2nd as well.  [Plain old common sense! \"If you've got both, you've either one, separately\".\r\n" );
document.write( "(1) \r\n" );
document.write( "1. S ∨ H \r\n" );
document.write( "2. B • E \r\n" );
document.write( "3. R ⊃ G \r\n" );
document.write( "4.   B    2, simp.\r\n" );
document.write( "5.   E    2, simp.\r\n" );
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document.write( "So if B is the 1st and E is the 2nd, then if you have\r\n" );
document.write( "the 1st and the 2nd, that guarantees that you have the 1st.\r\n" );
document.write( "It also guarantees that you have the 2nd.  [plain old common sense!]\r\n" );
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document.write( "(2) \r\n" );
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document.write( "\"CD\"  = constructive dilemma means \r\n" );
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document.write( "[(p ⊃ q) • (r ⊃ s) • (p ∨ r)] ⊃ (q ∨ s) \r\n" );
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document.write( "Think of ⊃ as the same as the word \"guarantees\".\r\n" );
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document.write( "When you know that\r\n" );
document.write( "(the 1st guarantees the 2nd) and (the 3rd guarantees the 4th) and \r\n" );
document.write( "you have (the 1st OR the 3rd), then that guarantees that you have either (the\r\n" );
document.write( "2nd or the 4th).\r\n" );
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document.write( "So below from 1 you have (N guarantees T) and (F guarantees Q), and from 3 you\r\n" );
document.write( "have (N or F), so that guarantees that you must have either T or Q, by\r\n" );
document.write( "constructive dilemma, CD.\r\n" );
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document.write( "1. (N ⊃ T) • (F ⊃ Q) \r\n" );
document.write( "2. (N ⊃ R) ∨ (F ⊃ M) \r\n" );
document.write( "3. N ∨ F \r\n" );
document.write( "4.   T V Q ,    1,2, CD\r\n" );
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document.write( "Logic is all common sense if you know and think about what the symbols mean.\r\n" );
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document.write( "Edwin
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