document.write( "Question 1209921: A. Use the first thirteen rules of inference to derive the conclusions of the following symbolized arguments:\r
\n" ); document.write( "\n" ); document.write( "1. (O v M) ⊃ S
\n" ); document.write( "2. ~S / ~M\r
\n" ); document.write( "\n" ); document.write( "1. ~(~E • ~N) ⊃ T
\n" ); document.write( "2. G ⊃ (N v E) /G ⊃ T\r
\n" ); document.write( "\n" ); document.write( "1. ~(F • A)
\n" ); document.write( "2. ~(L v ~A)
\n" ); document.write( "3. D ⊃ (F v L) /~D\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #851056 by CPhill(1959)\"\" \"About 
You can put this solution on YOUR website!
You've asked for the derivations again, and they're the same as before. Here they are, with the rules of inference clearly labeled:\r
\n" ); document.write( "\n" ); document.write( "**Argument 1:**\r
\n" ); document.write( "\n" ); document.write( "1. (O v M) ⊃ S
\n" ); document.write( "2. ~S / ~M\r
\n" ); document.write( "\n" ); document.write( "3. ~(O v M) **Modus Tollens (MT), 1, 2**
\n" ); document.write( "4. ~O • ~M **De Morgan's Theorem (DeM), 3**
\n" ); document.write( "5. ~M **Simplification (Simp), 4**\r
\n" ); document.write( "\n" ); document.write( "**Argument 2:**\r
\n" ); document.write( "\n" ); document.write( "1. ~(~E • ~N) ⊃ T
\n" ); document.write( "2. G ⊃ (N v E) / G ⊃ T\r
\n" ); document.write( "\n" ); document.write( "3. N v E **Double Negation (DN), ~(~E • ~N)**
\n" ); document.write( "4. G ⊃ ~(~E • ~N) **Hypothetical Syllogism (HS), 2, 3**
\n" ); document.write( "5. G ⊃ T **Hypothetical Syllogism (HS), 4, 1**\r
\n" ); document.write( "\n" ); document.write( "**Argument 3:**\r
\n" ); document.write( "\n" ); document.write( "1. ~(F • A)
\n" ); document.write( "2. ~(L v ~A)
\n" ); document.write( "3. D ⊃ (F v L) / ~D\r
\n" ); document.write( "\n" ); document.write( "4. ~L • ~~A **De Morgan's Theorem (DeM), 2**
\n" ); document.write( "5. ~L • A **Double Negation (DN), 4**
\n" ); document.write( "6. A **Simplification (Simp), 5**
\n" ); document.write( "7. ~F v ~A **De Morgan's Theorem (DeM), 1**
\n" ); document.write( "8. ~F **Disjunctive Syllogism (DS), 6, 7**
\n" ); document.write( "9. ~L **Simplification (Simp), 5**
\n" ); document.write( "10. F v L **Addition (Add), 8, 9**
\n" ); document.write( "11. ~D **Modus Tollens (MT), 3, 10**
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