Exclusive Or with Factor of Exclusive Or
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Theorem
- $\paren {p \oplus q} \oplus q \dashv \vdash p$
Proof
\(\ds \paren {p \oplus q} \oplus q\) | \(\dashv \vdash\) | \(\ds p \oplus \paren {q \oplus q}\) | Exclusive Or is Associative | |||||||||||
\(\ds \) | \(\dashv \vdash\) | \(\ds p \oplus \bot\) | Exclusive Or with Itself | |||||||||||
\(\ds \) | \(\dashv \vdash\) | \(\ds p\) | Exclusive Or with Contradiction |
$\blacksquare$
Sources
- 2012: M. Ben-Ari: Mathematical Logic for Computer Science (3rd ed.) ... (previous) ... (next): $\S 2.10$: Exercise $2.4$