Boolean Algebra optimization question

[FocusedWolf]

Hi,

This is a question about a boolean "law" type behavior I've noticed in my homework a couple of times.

Basically i can't find a boolean algebra law that permits this optimization short of using a k-map.

So I'm just wondering if theirs some way to optimize the one equation using just boolean algebra in order to get the second one (the output of the k-map).

 

[FocusedWolf]

Nvm i found it in the solutions for that homework.

It's called the "consensus theorem"

where:

xy' + xz' +y'z =xz' + y'z

Had a feeling it was some obscure identity/law lol

 

[FocusedWolf]

OK apparently theirs two or more forms: xy + x'z + yz = xy + x'z

found this one in a book, and matched wikipedia.