SOLUTION: 1. T ⊃ B Prove: L • B (Hint this involves using the Addition Rule) 2. T ⊃ ~X 3. T 4. X

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Question 1120001: 1. T ⊃ B Prove: L • B (Hint this involves using the Addition Rule)
2. T ⊃ ~X
3. T
4. X

Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!
1. T ⊃ B Prove: L • B (Hint this involves using the Addition Rule)
2. T ⊃ ~X
3. T
4. X
—————————————————————————————————
There is a logical contradiction in any attempted proof. Look at it. 


1.  T—>B       Premise

2.  T—>~X      Premise

3.  T          Premise

4.  X          Premise

5.  ~X         3,2  Modus Ponens (MP)

6.  X & (~X)   5,4  Contradiction — we must stop here!




Since the attempted proof contains a contradiction, one can not make a sound proof of  L & B.  Note that  another way to look at this:  it may be possible to "prove" L & B  but the proof will not be sound.   This is similar to proving 2=1 when there is a division by zero somewhere in the chain of reasoning.  





 

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