Simplify the following :

1. C+!(B*C)   2. (A+C)*(A*D+A*!D)+A*C+C = A+C
3. !(A*B)*(!A+B) = !A   4. A*(A+C)+(A+B)*(A+!B) = A


Try it before looking at answers


1. C+!(B*C) = 1

C+!(B*C)
  deMorgan
C+!B+!C
  Commutative
C+!C+!B
  Inverse
1 + !B
  Null
1
  
2. (A+C)*(A*D+A*!D)+A*C+C = A+C

(A+C)*(A*D+A*!D)+A*C+C
  Distribution
(A+C)*(A*(D+!D))+A*C+C
  Inverse
(A+C)*(A*(1))+A*C+C
  Identity
(A+C)*A+A*C+C
  Distribition
A*A+A*C+A*C+C
  Idempotent
A+A*C+C
  Identity
A*1+A*C+C
  Distribution
A*(1+C)+C
  Null
A*1+C
  Identity
A+C = A+C

3. !(A*B)*(!A+B) = !A

!(A*B)*(!A+B) = !A
  deMorgan
(!A+!B)*(!A+B)
  Distribution
!A*!A+!A*B+!A*!B+!B*B
  Inverse
!A*!A+!A*B+!A*!B+0
  Null
!A*!A+!A*B+!A*!B
  Distribution
!A*(!A+B+!B)
  Inverse
!A*(!A+1)
  Null
!A*(1)
  Indentity
!A
  
4. A*(A+C)+(A+B)*(A+!B) = A

A*(A+C)+(A+B)*(A+!B)
  Distribution
A*A+A*C+A*A+A*!B+A*B+B*!B
  Idempotent
A+A*C+A*!B+A*B+B*!B
  Identity
A*1+A*C+A*!B+A*B+B*!B
  Distribution
A*(1+C+!B+B)+B*!B
  Null
A*(1)+B*!B
  Null
A+B*!B
  Inverse
A+0
Null
A