document.write( "Question 1108255: How do I complete the following proofs?\r
\n" ); document.write( "\n" ); document.write( "Premises:
\n" ); document.write( "1. L ⊃ M
\n" ); document.write( "2. L
\n" ); document.write( "3. K v Q
\n" ); document.write( "4. ~K Prove: M ∙ Q\r
\n" ); document.write( "\n" ); document.write( "Premises:
\n" ); document.write( "1. (A v ~B) v C
\n" ); document.write( "2. ~A Prove: B ⊃ C\r
\n" ); document.write( "\n" ); document.write( "Premises:
\n" ); document.write( "1. M v N
\n" ); document.write( "2. O ⊃ ~N Prove: O ⊃ M
\n" ); document.write( "
\n" ); document.write( "

Algebra.Com's Answer #724348 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "Premises:\r\n" );
document.write( "\r\n" );
document.write( "1. L ⊃ M\r\n" );
document.write( "2. L\r\n" );
document.write( "3. K v Q\r\n" );
document.write( "4. ~K	           Prove: M ∙ Q\r\n" );
document.write( "\r\n" );
document.write( "5. M        1,2, Modus Ponens\r\n" );
document.write( "6. Q        3,4, Disjunctive Syllogism\r\n" );
document.write( "7. M ∙ Q    5,6, Conjunction \r\n" );
document.write( "\r\n" );
document.write( "---------------------------------\r\n" );
document.write( "\r\n" );
document.write( "Premises: \r\n" );
document.write( "1. (A v ~B) v C\r\n" );
document.write( "2. ~A             Prove: B ⊃ C\r\n" );
document.write( "\r\n" );
document.write( "3. A v (~B v C)     1, Association\r\n" );
document.write( "4. ~B v C         3,2, Disjunctive Syllogism\r\n" );
document.write( "5. B -> C           4, Material implication \r\n" );
document.write( "\r\n" );
document.write( "---------------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "Premises: \r\n" );
document.write( "1. M v N\r\n" );
document.write( "2. O ⊃ ~N	Prove: O ⊃ M\r\n" );
document.write( "\r\n" );
document.write( "3. N v M      1, Commutation\r\n" );
document.write( "\r\n" );
document.write( "              |4.   O     Assumption for Conditional Proof           \r\n" );
document.write( "              |5.  ~N     2,4, Modus Ponens\r\n" );
document.write( "              |6.   M     3,5, Disjunctive Syllogism   \r\n" );
document.write( "7. O ⊃ M    4-6  Conditional Proof\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );