[37-5] C: ~F ----------------------- 1: (F -> G) v H 2: ~G 3: ~H ---------------

Question

[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).

Explanation / Answer

37-5. Constructing truth table for the given argument:

F G F-> G ~F ~ G H ( F-> G) v H

T T T F F T T

T T F F F T T

F T T T T F T

F F T T T F T

thus the given argument is true as the conclusion either F->G or H follows from the premises about ~ G

and ~ H.

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