Provide a proof for the argument below: 1

Provide a proof for the argument below:

1. O -> N

2. ~M

3. S -> R

4. P -> O

5. R ->P

6. (S ->N) -> (M v L)             // ~P v L

Provide a proof for the argument below:

1. T v R

2. ~(S v ~R)

3. (T & S) -> ~Q

4. W -> Q                 // ~W

Provide a proof for the argument below:

1. B -> E

2. ~F v G

3. (B & C) &D

4. (C & D) -> F             // E & G

Translate the following argument into symbols using the letters provided, and then provide the proof demonstrating its validity:

No one can know anything, for every piece of reasoning must start somewhere.  And if every piece of reasoning must start somewhere, then every piece of reasoning begins with an unsupported premise.  Now, if every piece of reasoning begins with an unsupported premise, then all human thinking is based on mere assumption.  And if all human thinking is based on mere assumption, then no one can know anything. (S:  Every piece of reasoning must start somewhere; U: Every piece of reasoning begins with an unsupported premise; H: All human thinking is based on mere assumption; K: No one can know anything)