Question

1) Give a general proof to show that for all sentences X and Y and for every consistent set Σ of sentences, if X and Y are logical consequences of Σ, then the set {X, Y} is consistent.

2) Let C be a logical consequence of the set {P1, P2, P3} and of the set {P1, P2, not-P3}. Prove that C is a logical consequence of {P1, P2}.