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) :
1) AC + ABC + BC
A + C + ABC + BC -> De'Morgans
A + ABC + BC + C -> Commutative
A(1 + BC) + BC + 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 + AC
C(A * B + A) -> Distributive
C((A + A)(A + B)) -> Distributive
[simplified answer]? C * (A + B) -> Identity
4) BC + B(AD + CD)
BC + BAD + BCD -> Distributive
B(C + AD + CD) -> Distributive
..stuck~
5) (B + C + BC)(BC + AB + AC)
I basically tried to distribute everything.
Cancelled using identities and got stuck~
6) XYZ + XYZ + XYZ + XYZ
XZ + XYZ + XYZ -> Adjacency
XZ + X(YZ + YZ) -> Distributive
..stuck~ [Question: Can you simplify (YZ + YZ) to 1? (using the identity much similiar to X + X = 1)
7) XYZ + XYZ + XYZ + XYZ
XYZ + XYZ + XY -> Adjacency
Z(XY + XY) + XY -> Distributive
..stuck~ [Question: Can you simplify (YZ + YZ) to 1? (using the identity much similiar to X + X = 1)
Wow..that was tedious~
Well..there you go ^^;
Best regards~
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 + ABC + BC
A + C + ABC + BC -> De'Morgans
A + ABC + BC + C -> Commutative
A(1 + BC) + BC + 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 + AC
C(A * B + A) -> Distributive
C((A + A)(A + B)) -> Distributive
[simplified answer]? C * (A + B) -> Identity
4) BC + B(AD + CD)
BC + BAD + BCD -> Distributive
B(C + AD + CD) -> Distributive
..stuck~
5) (B + C + BC)(BC + AB + AC)
I basically tried to distribute everything.
Cancelled using identities and got stuck~
6) XYZ + XYZ + XYZ + XYZ
XZ + XYZ + XYZ -> Adjacency
XZ + X(YZ + YZ) -> Distributive
..stuck~ [Question: Can you simplify (YZ + YZ) to 1? (using the identity much similiar to X + X = 1)
7) XYZ + XYZ + XYZ + XYZ
XYZ + XYZ + XY -> Adjacency
Z(XY + XY) + XY -> Distributive
..stuck~ [Question: Can you simplify (YZ + YZ) to 1? (using the identity much similiar to X + X = 1)
Wow..that was tedious~
Well..there you go ^^;
Best regards~