Let $x$ be a set, $2^x=$ power $2 \mathrm{k}$ set of $\mathrm{X}$. define A binary operation $\Delta$ on $2^x$ as $A \Delta B=(A-B) \cup(B-A)$. Let $H=\left(2^x, \Delta\right)$, then
- for every $A \in 2^x$; inverse of $A$ is $\operatorname{not} A$.
- $\mathrm{H}$ is a group.
- $\mathrm{H}$ satisfies inverse prop, but not a group
- for every $A \in 2^x$; the inverse of $A$ is $A$.
