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Is it possible to find $a$ or $b$ given that $a \oplus b = c$ and $c \oplus b = a$ when I only have the value of $b$?

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  • $\begingroup$ I assume there's a typo in your question -- it's certainly possible to find $a$ or $b$ given the value of $b$! So I guess you want to find $a$ or $c$, or you're given $c$. Which is correct doesn't actually make any difference, though -- see my answer. $\endgroup$ – David Richerby Jan 11 '19 at 11:50
  • $\begingroup$ Also, does "find a or b" mean "find a and/or find b" or "find a$\lor$b"? (The current typesetting makes it look like the former but the original question just said find a or b. I guess the fact that "XOR" is capitalized but "or" isn't suggests that it's not the logical operator.) $\endgroup$ – David Richerby Jan 12 '19 at 14:23
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No. $a\oplus b = c$ and $c\oplus b = a$ are just rearrangements of the same equation, since

$$a\oplus b = c \iff (a\oplus b)\oplus b = c\oplus b\iff a=c\oplus b\,.$$

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