Lately I was trying to figure out some mathematical properties of XOR. So for equalities with XOR we can do $\oplus\ x$ on both sides of it and still get the right equality. Example:
$a \oplus b = c$
$a \oplus b \oplus b = c \oplus b$
$a = c \oplus b$
Will this work in inequalities? I mean, is it true that for any integers $a$, $b$, $c \geq 0$, if:
$a \oplus b < c$
$a > c \oplus b$
If not, what properties are there for inequalities with XOR?