I have trouble showing that
((p ∨ q) → r) → (p → (q ∨ r)) it is valid by means of a semantic table.
I know it's valid because I was able to test it using the following truth table:
As far as I know, a semantic table is a test of satisfaction. And a formula is valid if its denial is unsatisfactory. Therefore, I will need to construct a semantic table using formula negation and demonstrate that formula negation is unsatisfactory, making the formula valid.
So this was my attempt to build a semantic box for the formula:
My problem is that there is only one closed branch for this semantic box that I have built. And as far as I know, all branches must be closed so that this negation formula is not valid.
Any idea where I've strayed?