What does "≤⊕≥" mean?

Question

I just meet a symbol ≤⊕≥ in question "does the relation defined by (≤⊕≥) is the same as the relation ≠？", but I checked the Glossary of mathematical symbols, but did not find it, does anyone know it?

Answer 1

The symbol $⊕$ denotes XOR (exclusive or), so $\leq⊕\geq$ would denote $\leq$ XOR $\geq$. Let's create a table. Note that at least one of $\leq$ and $\geq$ must be true.

$\leq$	$\geq$	$\leq⊕\geq$	$\neq$
False	True	True	True
True	False	True	True
True	True	False	False

From this table, we can see that $\leq⊕\geq$ is logically equivalent to $\neq$. Hence, the answer is Yes.

Answer 2

$\leq⊕\geq$ means $\leq$ xor $\geq$. If you think about it, if $\leq$ is true but $\geq$ is not true, this will imply that $\neq$ must be true, or else both $\leq$ and $\geq$ will be true, and vice versa. If both $\leq$ and $\geq$ are true, this will impy that $=$ must be true, which in turn means that $\neq$ must be false. Clearly, $\neq$ is the same as $\leq⊕\geq$.