Boolean algebra question (1 Viewer)

[greekgun]

Ey guys, having abit of trouble with a question as was wondering if any1 could give me the answer to it plus the working out.

The question is:
Use the axioms (a)-(j) and the properties (k)-(u) to prove that in every Boolean algebra /(x+y/z) = /x/y/z + /x/yz + /xyz [where the slash infront of a term means "x bar" or "x compliment".]
Justify each line of your proof idicating what axiom/property you use.

I can kinda of do it, but i never get /x/y/z + /x/yz + /xyz as my answer.

 

[Suic1de]

Probably the wrong place to ask this question.

All IT people will have a different idea of what boolean even is.

 

[greekgun]

meh i couldnt figure out where to put it...it wouldn't go in science and engineering because this comes under discrete maths so i just took a guess.

 

[withoutaface]

/(x+y/z) = /x/y/z + /x/yz + /xyz

Use apostrophes.

(x + yz')' = x'(yz')' (de Morgans)
= x'(y'+z) (de Morgans)
= x'y' + x'z (distributive)
= x'y'*1 + x'z*1 (identity)
= x'y'(z+z') + x'z(y+y') (a+a'=1)
= x'y'z + x'y'z' + x'zy + x'zy' (distributive)
= x'y'z + x'y'z' + x'yz + x'y'z (commutative under multiplication)
= (x'y'z + x'y'z) + x'y'z' + x'yz (commutative under addition)
= x'y'z + x'y'z' + x'yz (a + a = a)
= x'y'z' + x'y'z + x'yz (commutative under addition)

 

[withoutaface]

There's also a few times I used the associative law in there, but you can figure that one out.

 

[Ben1220]

Probably the wrong place to ask this question.

All IT people will have a different idea of what boolean even is.

this area is for Computer Science too

and Boolean algebra is used alot in computer science. Look to the appendix section of any algorithm analysis/design or theory of computation book and there should be a section on boolean algebra.

Also many early computer science courses have a section on logic, including boolean algebra. For example 'Discrete structures' at melbourne uni. This is definently the right place for such a question