Just while reading, I saw that,
" For each $X≠∅$ subset of $N$ , $ (P(X), Δ)$ is subgroup of $(P(N), Δ)$"
I know all these notations, I mean, I know, the power set of natural numbers forms group with respect to the operation "symmetric difference Δ.
"My question is", why they had taken $X≠ ∅$ ? What if $X= ∅$ ? Is $(P(∅), Δ)$ is subgroup of $(P(N), Δ)$"? Or not?
My attempt: clearly $P(∅)= \{∅\}$ is nonempty subset of $P(N)$.
Further as,
$∅Δ∅ = (∅-∅) ∪ (∅-∅)$ $ = ∅∈ P(∅)$ Hence, $P(∅)$ is non empty, finite subset of $P(N)$, which is closed under the same binary operation as in $(P(N),Δ)$. Hence $(P(∅), Δ)$ is non-trivial subgroup of $(P(N), Δ)$.
Is am I right?