Proving universal sets Suppose A, B and C are sets in a universal set U, Show that:

I tried to solve, but unfortunately the results didn't come up...
I really need some help or guidance... 
 A: a.
$$[A\cap (B\cup C)]\cup[A^c\cap (B\cup C)]\cup (B\cup C)^c=$$
Using the distributive laws:
$$[(A\cap B)\cup (A\cap C)]\cup[(A^c\cap B)\cup (A^c \cap C)]\cup (B\cup C)^c=$$
Using the commutative laws:
$$[(A\cap B)\cup(A^c\cap B)] \cup [(A\cap C)\cup (A^c \cap C)]\cup (B\cup C)^c=$$
Using the distributive laws:
$$[B\cap (A\cup A^c)]\cup [C\cap (A\cup A^c)]\cup (B\cup C)^c =$$
Using the complement laws:
$$[B\cap U]\cup [C\cap U]\cup (B\cup C)^c =$$
Using the identity laws:
$$(B\cup C)\cup (B\cup C)^c=$$
Using the complement laws:
$$=U$$
b.
$$[A\cup (B\cap C)]\cap[A^c\cup (B\cap C)]\cap (B\cap C)^c=$$
Using the distributive laws:
$$[(A\cup B)\cap (A\cup C)]\cap[(A^c\cup B)\cap (A^c \cup C)]\cap (B\cap C)^c=$$
Using the commutative laws:
$$[(A\cup B)\cap(A^c\cup B)] \cap [(A\cup C)\cap (A^c \cup C)]\cap (B\cap C)^c=$$
Using the distributive laws:
$$[B\cup (A\cap A^c)]\cap [C\cup (A\cap A^c)]\cap (B\cap C)^c =$$
Using the complement laws:
$$[B\cup \emptyset]\cap [C\cup \emptyset]\cap (B\cap C)^c =$$
Using the identity laws:
$$(B\cap C)\cap (B\cap C)^c=$$
Using the complement laws:
$$=\emptyset$$
