Proof by natural deduction

Question

1. (~F v X) ↄ (P v T)

2. F ↄ P

3. ~P /T

Answer 1

Thanks to premise 3, we are allowed to conclude, via modus tollens, that ~F

4 ~F MT 2, 3

The rule of Addition allows us to add any "or" statement to a statement we know to be true

5 ~F v X Add 4

This satisfies the condition in premise 1. By modus ponens, PvT

6 PvT MP 1, 5

But remember premise 3? It says that ~P. Therefore

7 T DS 3, 6

QED = Quod erat demonstrandum