# Problem with boolean algebra!

mr_coffee
Hello everyone I'm having problems proving this:
note: A' will stand for complemented;

AB + BC'D' + A'BC + C'D = B + C'D
B(A+C'D')
B(A+C'+D')
BA + BC' + BD' + A'BC + C'D
BA + BD' + A'BC + C'(B+D)
B(A + D' + A'C) + C'(B+D)
now I'm stuck, i don't see how that is going to work out. Any help would be great.

Mentor
It works on a Karnaugh map. Try mapping it out to help you with the algebra. Look for combinations on the map that you can use as tricks in the algebraic manipulations.

abdo375
OK this is going to be long but i but a lot off steps for explanation so you can skip some
steps

AB+BC'D'+A'BC+C'D
B(A+A'C)+BC'D'+C'D
B((A+A').(A+C))+BC'D'+C'D
B((1).(A+C))+BC'D'+C'D
AB+BC+BC'D'+C'D
B(C+C'D')+AB+C'D
B((C+C').(C+D'))+AB+C'D
BC+BD'+AB+C'D
BC.(D+D')+BD'+AB+C'D
BCD+BCD'+BD'+AB+C'D
BCD+BD'+AB+C'D
D(C'+BC)+BD'+AB
D((C'+C).(C'+B))+BD'+AB
D((1).(C'+B))+BD'+AB
CD'+BD+BD'+AB
C'D+B+AB
B(A+1)+C'D
B+C'D = RHS

mr_coffee
awesome, thanks for the help guys!

abdo375