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
