Is $((A\to B)\land (\lnot A \to C))\equiv (A\lor C)$?

Question

I'm wondering whether $((A\to B)\land (\lnot A \to C)) \iff (A\lor C)$ is correct or not.

Have you tried using a truth-table? If not, what else have you tried? — amWhy, Jan 08 '17 at 23:29
Since $(\lnot A \to C) \equiv (A\lor C)$, we have $((A\to B) \land (\lnot A \to C)) \rightarrow (A\lor C))$, But not vice-versa. So the biconditional is wrong. — amWhy, Jan 08 '17 at 23:45

score 2 · Answer 1 · answered Jan 08 '17 at 23:41

2

Hint:

$\neg A \Rightarrow C$ is equivalent to $A\vee C$.

answered Jan 08 '17 at 23:41

Jacky Chong

score 2 · Answer 2 · answered Jan 08 '17 at 23:47

2

Hint: Consider the case $A:\text{true}$, $B:\text{false}$, $C:\text{any}$

answered Jan 08 '17 at 23:47

robjohn

2 Answers2