1. ~A ∴ [(A • B) ⋁ (C • D)] ↔ [(A ⋁ C) • (A ⋁ D)]
2. (A • B) ⋁ (C • D) Assume (CP)
3. ~A Assume (CP)
4. ~A ⋁ ~B 3, Add
5. ~(A • B) 4, DeM
6. C • D 2, 5, DS
7. ~A → (C • D) 3–6, CP
8. ~~A ⋁ (C • D) 7, MI
9. A ⋁ (C • D) 8, DN
10. (A ⋁ C) • (A ⋁ D) 9, Dist
11. [(A • B) ⋁ (C • D)] → [(A ⋁ C) • (A ⋁ D)] 2–10, CP
12. (A ⋁ C) • (A ⋁ D) Assume (CP)
13. A ⋁ (C • D) 12, Dist
14. C • D 13, 1, DS
15. (A • B) ⋁ (C • D) 14, Add
16. [(A ⋁ C) • (A ⋁ D)] → [(A • B) ⋁ (C • D)] 12–15, CP
17. [(A • B) ⋁ (C • D)] → [(A ⋁ C) • (A ⋁ D)] •
[(A ⋁ C) • (A ⋁ D)] → [(A • B) ⋁ (C • D)] 11, 16, Conj
18. [(A • B) ⋁ (C • D)] ↔ [(A ⋁ C) • (A ⋁ D)] 17, ME
1 comment:
I'm crying so hard. There's diarrhea everywhere. I'm so proud of you. Love you!
Post a Comment