SOLUTION: Construct a formal proof of validity for the following argument ~B v [(C⊃D) · (E⊃D)] B · (C v E) Therefore, D

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Question 1144033: Construct a formal proof of validity for the following argument
~B v [(C⊃D) · (E⊃D)]
B · (C v E)
Therefore, D
Answer by math_helper(2461) About Me  (Show Source):
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Construct a formal proof of validity for the following argument
~B v [(C⊃D) · (E⊃D)]
B · (C v E)
Therefore, D 


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NOTE: Using

  & for "AND" 

  v for "OR"

  --> for  "implies"

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1. ~B v ((C-->D) & (E-->D))  Premise

2. B & (C v E)               Premise

3. B                         2 Simplification (SIMP)

4. ((C-->D) & (E-->D))       3,1 Conditional Disjunction (CD)

5. C v E                     2 SIMP

6. :: C                      Conditional Proof (CP) assumption #1

7. :: D                      6,4 Modus Ponens (MP)

8. :: E                      CP assumption #2

9. :: D                      8,4 MP

10.:: (C V E) --> D          6-9 Proof by Cases (PBC)

11. D                        5,6-10  CP