Logic: Proving tautological consequence
I'm having trouble proving this tautological consequence. I'd hope that you guys can maybe oversee my process and identify errors, because I went over this couple of times and I arrive at the same conclusion.
The question goes like this:
> $A \Rightarrow B$
>
> $C \Rightarrow B$
>
> Therefore: $(A \lor C) \Rightarrow B$
>
> Q: Show that the conclusion of the arguments is a tautological consequence of the premises using truth tables.
This is how I tried to solve it:
My solution to the problem. It seems like I'm missing something very fundamental here.
make a truth table of $$((a \rightarrow b) \land (c \rightarrow b)) \rightarrow ((a \lor c) \rightarrow b)$$