# Find value of $a$ or $b$ of two XOR equations

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 $$b$$?

• 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. – David Richerby Jan 11 '19 at 11:50
• 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.) – David Richerby Jan 12 '19 at 14:23

No. $$a\oplus b = c$$ and $$c\oplus b = a$$ are just rearrangements of the same equation, since
$$a\oplus b = c \iff (a\oplus b)\oplus b = c\oplus b\iff a=c\oplus b\,.$$