SOLUTION: 1. A v B 2. A ≡ (C & D) 3. B ⊃ (D & G)/D I know I need to use indirect proof to derive the conclusion but I am thrown off by the ≡ symbol as we rarely have used that s

Algebra ->  Proofs -> SOLUTION: 1. A v B 2. A ≡ (C & D) 3. B ⊃ (D & G)/D I know I need to use indirect proof to derive the conclusion but I am thrown off by the ≡ symbol as we rarely have used that s      Log On


   

Question 1171838: 1. A v B
2. A ≡ (C & D)
3. B ⊃ (D & G)/D
I know I need to use indirect proof to derive the conclusion but I am thrown off by the ≡ symbol as we rarely have used that symbol
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Note:
With "Material Equivalence" you can replace 

p ≡ q   by  (p ⊃ q) & (q ⊃ p)


1. A v B 
2. A ≡ (C & D) 
3. B ⊃ (D & G)      /D

                | 4. ~D                 Assumption for Indirect Proof
                | 5. [A ⊃ (C & D)] & [(C & D) ⊃ A) 2, Material Equivalence 
                | 6. ~D v ~C                        4, Addition
                | 7. ~C v ~D                        6, Commutation
                | 8. ~(C & D)                       7, DeMorgan's law
                | 9. A ⊃ (C & D)                    5, Simplification
                |10. ~A                             9,8, Modus tollens
                |11. B                              1,10, Disjunctive Syllogism  
                |12. D & G                          3,11, Modus ponens
                |13. D                              12, Simplification
                |14. D & ~D                         13,4, Conjunction
15. D                Lines 4-14  Indirect Proof

Edwin