*hi guys ^^;*

well.. i am new here and would greatly appreciate some help with the following algebra simplification problems (i have included my work so that i may compare the logic with you guys):

well.. i am new here and would greatly appreciate some help with the following algebra simplification problems (i have included my work so that i may compare the logic with you guys)

**1)**

__AC__+__A__BC +__B__C__A__+

__C__+

__A__BC +

__B__C -> De'Morgans

__A__+

__A__BC +

__B__C +

__C__-> Commutative

__A__(1 + BC) +

__B__C +

__C__-> Distributive

..stuck~

**2) (**

__A+B__)(__A__+__B__)(

__A__*

__B__)(

__A__+

__B__) -> De'Morgans

(

__A__*

__A__*

__B__) + (

__A__*

__B__*

__B__) -> Distributive

[simplified answer]?

__A__+

__B__-> Identity

**3) ABC +**

__A__CC(A * B +

__A__) -> Distributive

C((

__A__+ A)(

__A__+ B)) -> Distributive

[simplified answer]? C * (

__A__+ B) -> Identity

**4) BC + B(AD +**

__C__D)BC + BAD + B

__C__D -> Distributive

B(C + AD +

__C__D) -> Distributive

..stuck~

**5) (B +**

__C__+ B__C__)(BC + A__B__+ AC)I basically tried to distribute everything.

Cancelled using identities and got stuck~

**6)**

__XYZ__+__X__Y__Z__+ X__Y__Z + XY__Z____XZ__+ X

__Y__Z + XY

__Z__-> Adjacency

__XZ__+ X(

__Y__Z + Y

__Z__) -> Distributive

..stuck~ [Question: Can you simplify (

__Y__Z + Y

__Z__) to 1? (using the identity much similiar to X +

__X__= 1)

**7)**

__X__Y__Z__+ X__YZ__+ XY__Z__+ XYZ__X__Y

__Z__+ X

__YZ__+ XY -> Adjacency

__Z__(

__X__Y + X

__Y__) + XY -> Distributive

..stuck~ [Question: Can you simplify (

__Y__Z + Y

__Z__) to 1? (using the identity much similiar to X +

__X__= 1)

*Wow..that was tedious~*

Well..there you go ^^;

Best regards~

Well..there you go ^^;

Best regards~