I was wondering about this question.
Logically, I would like to say that in every boolean algebra that is true.
Because: $x\oplus0=x·0'+x'·0 = x·0'$.
And in the binary boolean algebra that is correct as: $0'=1 \rightarrow x·0'=x·1=x$
But is that true for ANY of it?
I would love some insight from you, thank you!
From the axioms of a boolean algebra, we have $$\lnot0=\lnot0\lor0=1$$ and $$x\land0=0\land x=0\land(0\lor x)=0,$$ so if $x\oplus y$ is defined as $(x\land\lnot y)\lor(\lnot x\land y)$, then we have $$x\oplus0=(x\land\lnot 0)\lor(\lnot x\land 0)=(x\land1)\lor0=x.$$