I am struggling with logical formula equivalence. I need to transform logical formula
$(A \wedge B \wedge C) \vee (A \wedge B \wedge \neg C) \vee (A \wedge \neg B \wedge \neg C) \vee (\neg A \wedge \neg B \wedge C)$
to
$A \iff (C \implies B)$
Can someone help me with this, please? I am currently stuck at:
$(A \vee \neg B) \wedge ((A \wedge B) \vee ((A \wedge \neg C) \vee (\neg A \wedge C))$
Thanks, Frank.
Since we have $(B\land C), \ (B\land\lnot C), \ (\lnot B\land\lnot C), \ (\lnot B\land C) $ pairwise disjoint, and their union is the constant True, the conjunction of the first three terms is $A\land(\lnot (\lnot B\land C))$ which equals to $A\land(B\lor\lnot C) \ =\ A\land(C\to B) $.
The forth term is $\lnot A\land\lnot(B\lor\lnot C) \ =\ \lnot A\land\lnot(C\to B) $.
Finally, we have $A\leftrightarrow D\ =\ (A\land D) \lor(\lnot A\land\lnot D)$.