I'm reviewing my previous exams for the final, and the only two true or false questions that confuse me are:
If (A⊃B)∨(A⊃C) is true, then A implies either B or C.
(P⊃Q)∨(P⊃~Q) means P⊃(Q∨~Q).
The answer is that both statements are false.
For 1, ((A⊃B)∨(A⊃C))⊃(A⊃(B∨C)), either by assigning truth values or by proof using inference, I find the conditional to be a tautology.
For 2, both (P⊃Q)∨(P⊃~Q) and P⊃(Q∨~Q) are tautologies. So ((P⊃Q)∨(P⊃~Q)) is equivalent to (P⊃(Q∨~Q)).
Then, why are these two statements false?