document.write( "Question 1193420: Prove the following using conditional proof:\r
\n" ); document.write( "\n" ); document.write( "1. ∼A ⊃ (B • C)
\n" ); document.write( "2. D ⊃ ∼C / D ⊃ A \n" ); document.write( "

Algebra.Com's Answer #825441 by math_tutor2020(3816) $\"\"$ $\"About$

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Number		Statement	Line(s) Used	Reason
1		~A -> (B & C)
2		D -> ~C
	:.	D -> A
	3	D		Assumption for Conditional Proof
	4	~C	2,3	Modus Ponens
	5	~C v ~B	4	Addition
	6	~B v ~C	5	Commutation
	7	~(B & C)	6	De Morgan’s Law
	8	~~A	1,7	Modus Tollens
	9	A	8	Double Negation
10		D -> A	3-9	Conditional Proof

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\n" ); document.write( "\n" ); document.write( "In line 3, I have the antecedent D as the assumption to start the conditional proof off.
\n" ); document.write( "We simply start with the \"if\" part of the \"if, then\" conditional in the conclusion.
\n" ); document.write( "So we assume that the logical statement D is the case.
\n" ); document.write( "Somehow we have to arrive at statement A based on this key assumption.\r
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\n" ); document.write( "\n" ); document.write( "That's exactly what this derivation table does. The proof more or less starts at line 3, while working its way down until reaching line 9 where we arrive at statement A.
\n" ); document.write( "Collectively lines 3 through 9 all group together to show D leading to A, therefore D -> A\r
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\n" ); document.write( "\n" ); document.write( "I'm using arrow symbols in place of the horseshoe symbols.
\n" ); document.write( "Also, I used ampersands in place of the dot symbols.
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