If ya'll get bored and wanna read more about this, this is a property called functional completeness. I'm pretty sure nand and nor are the only functionally complete binary operators, so xor shouldn't be functionally complete.
<span style="color:#323232;">A | B | A => B
</span><span style="color:#323232;">T T T
</span><span style="color:#323232;">T F F
</span><span style="color:#323232;">F T T
</span><span style="color:#323232;">F F T
</span>