The roots of, let's say 4, can be either 2 or -2. Why is this an inclusive-or i.e. if $x^2 = 4$, then $x = 2 \vee x = −2$, instead of an exclusive-or i.e. if $x^2 = 4$, then $x = 2 \oplus x = −2$? It can only be one of them because we can only get 4 if we do a $2 \times 2$ or a $-2 \times -2$. From my understanding, something that can only be one or the other, should be treated as an exclusive-or.
Thanks in advance!