SOLUTION: Solve the following by using only the 18 rules of implication and replacement to get: (H • U) ⊃ (S • D) 1. H ⊃ D 2. U ⊃ S

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Question 1190083: Solve the following by using only the 18 rules of implication
and replacement to get: (H • U) ⊃ (S • D)
1. H ⊃ D
2. U ⊃ S

Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
Solve the following by using only the 18 rules of implication
and replacement to get: (H • U) ⊃ (S • D)
   1. H ⊃ D
   2. U ⊃ S

   3. (H ⊃ D) • (U ⊃ S)                  1,2 Conjunction 
   3. [(H ∨ U) ⊃ D] • [(U ∨ H) ⊃ S]      2,  Addition
   4. [~(H ∨ U) ∨ D] • [~(U ∨ H) ∨ S]    3, Material implication 
   5. [~(H ∨ U) ∨ D] • [~(H ∨ U) ∨ S]    4, Commutation
   6. ~(H ∨ U) ∨ (D • S)                 5, Distribution 
   7. (H ∨ U) ⊃ (D • S)                  6, Material implication
   8. (H • U) ⊃ (H ∨ U)                  Conjunction implies Disjunction
   9. (H • U) ⊃ (D • S)                  8,7, Hypothetical syllogism 
  10. (H • U) ⊃ (S • D)                  9. Commutation

Edwin
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