SOLUTION: 1) A v B 2) B > (A v D) 3) ~D Conclusion: A

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Question 1112733: 1) A v B
2) B > (A v D)
3) ~D
Conclusion: A
Answer by math_helper(2461) About Me  (Show Source):
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1) A v B
2) B > (A v D)
3) ~D
Conclusion: A
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1.  AvB     Premise   

2. B—>(AvD) Premise

3. ~D       Premise

4. :: B     Assumption, begin conditional proof (CP) - Case 1

5. :: AvD   4,2  Modus Ponens (MP)

6. :: A     3,5  Disjunctive Syllogism (DS)

7.  :: ~B   Assumption. Case 2

8. ::  A    7,1    DS

9. A        6,8   Proof By Cases (PBC), end of CP,  (A is true under no assumptions)