document.write( "Question 1171728: 1. J => (L v T) Basic Assumption
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Algebra.Com's Answer #796647 by math_helper(2461) $\"\"$ $\"About$

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document.write( "1. J ==> (L v T)      Premise
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document.write( "2.  ~(L v ~J)         Premise
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document.write( "// Prove: ~L ==> T\r
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document.write( "3. ~L & J             2, DeMorgan's (DeM)
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document.write( "4. J                  3, Simplification (SIMP)
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document.write( "5. L v T              4,1, Modus Ponens (MP) 
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document.write( "6. ~L ==> T           5, Material Implication (MI)\r
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document.write( "---------- DONE ----------\r
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document.write( "In words:
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document.write( "3.  \"Not (L or (not J))\" true means we can say equivalently \"(not L) AND (J)\" is true.  Draw a truth table if not convinced.
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document.write( "4.  Since \"(not L) and J\" is true, we can say \"J is true\" (we can also say \"not L\" is true but we don't need that in this proof).
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document.write( "5.  Given J is true, it follows \"L or T\" is true, by premise #1.
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document.write( "6.  \"L or T\" true is the same as  \"if (not L) then T\".   Draw a truth table if not convinced.  \r
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