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Simplify the following expressions using Boolean Algebra :-

 

  •  A + AB

= A.1+AB
= A(1+B)                            :-  OR (A+1 = 1)
= A.1
= A

 

  • AB+AB’

= A(B+B’)                            :- AB+AC = A(B+C)
= A(B+B’)                           :-  A + A’ =1
= A(1)
= A

  • A’BC + AC

= C(A’B+A)                         :- A+BC =  (A+B).(A+C)
= C((A’+A).(A+B))             :- A’+A=1
= C(1.(A+B))
= C(A+B)

 

  • A’B+ABC’+ABC

= A’B+AB(C’+C)                       :- A’+A=1
= A’B+AB
= B(A’+A)                                   :- A’+A=1
= B

  • A’ B’ C + A’ B C’ + A B’ C’ + A B C

 

= A’(B’C+BC’)+A(B’C’+BC)            :-  A’B+AB’ = A XOR B     , A’B+AB’ = (A XOR B)’
=A’(B XOR C) + A((B XOR C)’)      :-    let B XOR C = T ,   A’T+AT’ which implies  =A XOR T
= A XOR T                                                :-  T = B XOR C

 

=A XOR B  XOR C
 
Note: It is illustrated for beginners

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