Derive the conclusions from the premises in the arguments below by utilizing inference rules: ====================================== [37-1] C: G --------------------- 1: ~M 2: N -> G 3: N v M --------------------- ====================================== [37-2] C: D ----------------------- 1: ~G -> (A v B) 2: ~B 3: A -> D 4: ~G ----------------------- ====================================== [37-3] C: ~B ------------------------ 1: A -> (B -> C) 2: ~C 3: ~D -> A 4: C V ~D ------------------------ ====================================== [37-4] C: D & E ----------------------- 1: A -> (~B & C) 2: C -> D 3: E v B 4: A ====================================== [37-5] C: ~F ----------------------- 1: (F -> G) v H 2: ~G 3: ~H ----------------------- ====================================== [37-6] C: L ---------------------- 1: ~A 2: (C v A) -> L 3: A v D 4: (D v U) -> C ---------------------- ----------------------------------------------------------------------------- 3. convention for proof Unlike using TT for validity, doing proof is more detailed in that it provides a series of steps extending the truth values stored in premises all the way to the conclusion; each step is to be justified by reference to the two things: 1. the inference rules employed for the new step 2. the premises (or statements produced at previous stages) employed for the new step The reference to these two items should be accompanied to each step. Follow and adopt the convention for proof. This is the most distinctively powerful phase of studying formal logic (equivalent or similar to algorithmic thinking in computer science and math).