I'm trying to study for my midterm and I need help figuring out what to do for this problem. It says:
Determine whether the following statement is correct, using any legitimate truth-table technique.
~A ∨ (B → C), E → (B & A), C → E |= C ↔ A
I make a truth table for each statement but I don't how the main connective correlates with the other connectives in the other statements.
I think I have to make a joint table but I really don't know where to begin. If anyone can help me understand it would be greatly appreciated!
A,B,C |= D means that if A,B,C are all true then D is true as well. But, this is exactly what the expression (A & B & C) -> D says. Thus A,B,C |= D is true if and only if (A & B & C) -> D is a tautology. In other words, the connective -> captures the meaning of |=. For your problem, you can make a truth table for the compound expression
[(~A ∨ (B → C)) & (E → (B & A)) & (C → E)] -> (C ↔ A)
and see if it is a tautology