# Boolean Algebra: Operation Linkage Laws

Im studying some properties of Boolean Algebra and found the Operation Linkage Laws.

Im not able to understand how this laws are possible, and the remark on the proof is not really clear for me. Can any one show me the proofs of this laws or share any resources where I can find a more detailed proof of the laws?

• Please transcribe the image as text, to enable textual search. Jan 22 '17 at 22:07

What the comment is trying to explain is that, say, $xy=x$ isn't universally true (consider $x=0,y=1$). However, if $xy=x$ then also $x+y=y$, and vice versa. This is in contrast to identities such as $x+x=x$, which always hold (for all values of $x$).