I've just started learning boolean algebra at university and am stuck by the following problem:

Prove the identity a.b + a'.c = (a+c).(a'+b) using boolean algebra.

Could somebody please give me a push in the right direction?

Thanks in advance.

 

Why don't you make a truth table out of the right expression and solve it using a Karnaugh map. Boolean operations won't get you where you want easilly.

 

a.b + a'.c = (a+c).(a'+b)
(a+c).(a'+b) = (a+c).a' + (a+c).b = a.a' + c.a' + a.b + c.b
a.a' = F

so (a+c).(a'+b) = F + c.a' + a.b + c.b = c.a' + a.b + c.b = a.b + a'.c + c.b= a.b + a'.c + c.b(a+a') = a.b + a'.c + c.b.a+c.b.a' = a.b + c.b.a+ a'.c +c.b.a' = a.b( 1 + c) + a'.c(1+b) =a.b + a'.c

works both ways

 

ummm...?? What ??????