SOLUTION: Prove directly, no Conditional Proof or Indirect Proof 1. I ∨ (N • F) 2. I ⊃ F / F

Question 1193812: Prove directly, no Conditional Proof or Indirect Proof
1. I ∨ (N • F)
2. I ⊃ F / F
Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!

I'll go over the outline of what the derivation would look like.
This will be an informal paragraph format rather than a formal derivation table, which I'll let you do.

The conclusion we want to derive is the statement F
It's an unfortunate choice of symbol because F is often used to mean "False".

We can use the distributive rule for premise 1 to go from
I v (N • F)
to
(I v N) • (I v F)
The first part I v N isn't all that useful
The second part I v F can be picked out using the simplification rule.

Then notice how I v F is the same as ~~I v F and that turns into ~I ⊃ F through the material implication rule.
Flip things around (transposition rule) to get ~F ⊃ ~~I or ~F ⊃ I

We have these statements to focus on
~F ⊃ I (what we just found)
I ⊃ F (premise 2)

The hypothetical syllogism rule then allows us to combine those two conditionals into ~F ⊃ F
This turns into ~~F v F or F v F or simply F
The proof is concluded.

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