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Hi can anyone help me with this problem? Would greatly be appreciated.

  1. M → I

  2. ¬ I ∧ L

  3. M ∨ B

Prove: B

  • Hint: you can get B if you get ~M. You can get ~M from 1 and 2. – Eliran Apr 23 '19 at 22:44
  • 2
    Hi, welcome to Philosophy SE. First, we do not know what course you are taking and where you are at in it, hence what rules you are allowed to use. You have to describe that in your post. For example, ¬ I → ¬M follows from 1 by contrapositive, then 2 gives you ¬M by conjunction elimination, and ¬M together with 3 gives you B by a simple instance of resolution, but who knows what your instructor expects. And second, we tend not to do HW for people, but we can help if you describe what you tried. – Conifold Apr 23 '19 at 22:48
  • Oh Im sorry I didnt know. I just have been having a hard time and hoped I can finally see how to crack this problem so I can tackle others and use what I learned here. – Hamish Docherty Apr 23 '19 at 23:22
1

Use a Proof by Cases (Disjunction Elimination).

|   M → I
|   ¬ I ∧ L
|_  M ∨ B 
|    |_  M         assumption
|    |    :         
|    |    :
|    |    B          for some reason
|    M → B      conditional introduction
|    |_  B         assumption
|    B → B      conditional introduction
|    B               disjunction elimination
| improve this answer | |

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