303a6solns - ASSIGNMENT 6 SOLUTIONS MATH 303, FALL 2011 If...

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Unformatted text preview: ASSIGNMENT 6 SOLUTIONS MATH 303, FALL 2011 If you find any errors please let me know Manipulation (M1) By rule C we have that (( c = d ) ( d = c )) c = c is valid. Then by rule F applied with A ( x ) being (( c = x ) ( x- c )) and B being c = c we get that x (( c = x ) ( x = c )) c = c is valid, which is what we were supposed to show. (M2) First notice that by Cohens definition of derive the question is asking if ( xA ( x ) ( A ( c ) B )) B is valid. By rule E we know that xA ( x ) A ( c ) is valid. Consider the following formula ( xA ( x ) A ( c )) (( xA ( x ) ( A ( c ) B )) B ) Letting C be xA ( x ) this is the formula ( C A ( c )) (( C ( A ( c ) B )) B ) This is a propositional function in the letters C , A ( c ), and B , so we can apply rule A. To do this build a truth table (unfortunately a bit of a large one) A ( c ) B C C A ( c ) A ( c ) B C ( A ( c ) B ) ( C ( A ( c ) B )) B whole thing F F F T T F T T F F T F T T F T F T F T T F T T F T T F T T T T T F F T F F T T T F T T F F T T T T F T T F T T T T T T T T T T We see that the propositional function in question is identically true, so by rule A it...
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This note was uploaded on 01/30/2012 for the course MATH 310 303 taught by Professor Rwk during the Spring '11 term at Simon Fraser.

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303a6solns - ASSIGNMENT 6 SOLUTIONS MATH 303, FALL 2011 If...

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