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

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There is a logical contradiction in any attempted proof.  Look at it.  

<pre>
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!<br>

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.