Exclusive Or Properties
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Theorem
Exclusive Or is Commutative
- $p \oplus q \dashv \vdash q \oplus p$
Exclusive Or is Associative
- $p \oplus \paren {q \oplus r} \dashv \vdash \paren {p \oplus q} \oplus r$
Exclusive Or with Itself
Exclusive or destroys copies of itself:
- $p \oplus p \dashv \vdash \bot$