Basic set theory question about complement

[damightytom]

Homework Statement

Hi I could use some help getting an explanation that kinda twists my head a bit.
I want to know what I'm missunderstanding so I can get this right from the beginning.
^c = complement
U = union

I want to simplify this set
A U (A U B^c)^c intersect (A U C )
to
AU(BnC)
Using set theory laws

The Attempt at a Solution

So I start using set theory rules.

De Morgans
A U (A^c intersect B) intersect (A U C)

Distributive Law
A U (A^c intersect B) intersect C)

This seem to be the same as AU(BnC), so it seems A^c doesn't have any impact.
When using the distributive law can I do like this?
A U ((B^c)^c intersect C)
I would really appreciate any explanation on why this is and if there's any fault in my logic.
Thanks

 

[Andrax]

Homework Statement

Hi I could use some help getting an explanation that kinda twists my head a bit.
I want to know what I'm missunderstanding so I can get this right from the beginning.
^c = complement
U = union

I want to simplify this set
A U (A U B^c)^c intersect (A U C )
to
AU(BnC)
Using set theory laws

The Attempt at a Solution

So I start using set theory rules.

De Morgans
A U (A^c intersect B) intersect (A U C)

Distributive Law
A U (A^c intersect B) intersect C)

This seem to be the same as AU(BnC), so it seems A^c doesn't have any impact.
When using the distributive law can I do like this?
A U ((B^c)^c intersect C)
I would really appreciate any explanation on why this is and if there's any fault in my logic.
Thanks

you know that A^cB <=> A Intersect B barre*
Relationships between relative and absolute complements:
A ∖ B = A ∩ Bc (Bc is the elements out of the set b )
*sorry we read math in french don't know how to explain it it's b with a line
check this article on wikipedia http://en.wikipedia.org/wiki/Complement_(set_theory )
at Relationships between relative and absolute complements: