The Power of Logic

After a long absence from blogging, I have the itch.

To explain my absence let me explain my life. School is absolute insanity. This is the hardest semester to date and I am on the razor's edge of a mental breakdown. I am taking Media Law and Ethics, Advanced Theory of International Relations, Logic, Business Law, and Advanced American Foreign Policy. 15 credits. Doesn't seem so bad eh??? DON'T BE DECEIVED.

This is the story of my life!

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