- #1

damightytom

- 17

- 0

## 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