In: Advanced Math
1. ¬B∨(G↔J), H→(B&C) ∴(H&J)→G
2. A∨B, C↔¬(B∨D) ∴C→A
3. (A&B) ↔ (F→G), (A&F) & B∴(G→R)→R
4. T→¬B, T→¬D ∴ T→¬(B∨D)
5. ¬(M∨¬S), S→(R→M) ∴A → (¬R∨T)
6. (F&G) → I, (I∨J) → K ∴F→(G→K)
7. ¬U, O→G, ¬(O∨G) →U ∴G
Prove that the arguments are valid by constructing a dedication using the rules MP, MT, DN, Conj, Simp, CS, Disj, DS, DM, CP, HS, BE, and DL. Use CP if needed.