Normal Form (Logic and sets) Using distribution laws the following
G <=> (A ^B^(¬C)) ˇ ((¬A)^B^C) ˇ ((¬A)^(¬B)^C) ˇ ((¬A)^(¬B)^(¬C))
"can be written" as 
G <=> (A ^B^(¬C)) ˇ ((¬A)^B^C) ˇ ((¬A)^(¬B)) ˇ (Cˇ(¬C))
and (Cˇ(¬C)) is always true, we can write 
G <=> (A ^B^(¬C)) ˇ ((¬A)^B^C) ˇ ((¬A)^(¬B)) 
which I understand, but the second row is what I can't understand. 
It's taken from my professors Analysis script. 
Can somebody break it down?
 A: The manipulation of the first line into the second only concerns the last two terms, let's say $S$.
$$S=(\neg A\land\neg B\land C)\lor(\neg A\land\neg B\land\neg C)$$
Perhaps it'll be clearer to see how the next line is gotten if you let $D=\neg A\land\neg B$, and hence
$$S=(D\land C)\lor(D\land\neg C)$$
$$=D\land (C\lor\neg C)$$
$$=(\neg A\land\neg B)\land (C\lor\neg C)$$
A: 
Using distribution laws the following
$G \iff (A \land B\land \lnot C) \lor (\lnot A\land B\land C) \lor (\lnot A\land \lnot B\land C) \lor (\lnot A\land \lnot B\land\lnot C)$
"can be written" as
$G \iff (A \land B\land \lnot C) \lor (\lnot A\land B\land C) \lor (\lnot A\land \lnot B) \lor (C\lor \lnot C)$

$\require{enclose}G \iff (A \land B\land \lnot C) \lor (\lnot A\land B\land C) \lor ((\lnot A\land \lnot B){\enclose{circle}[color:red]{\bbox[0.25ex, color:black]\land}} (C\lor \lnot C))$

and $C\lor ¬C$ is always true, we can write
$G \iff (A \land B\land \lnot C) \lor (\lnot A\land B\land C) \lor (\lnot A\land\lnot B)$
which I understand, but the second row is what I can't understand.

That's possibly because you miscopied.
