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I can thnk of only one way to tackle this problem, however, it is very tedious. $$ a \oplus b \iff (a \land \neg b) \lor(\neg b \land a)$$ And so now I evaluate, by definition, $(a \oplus b) \oplus c$ and $a \oplus(b\oplus c)$ And then, using the associativity of OR and AND, I get the same expression for arrangements of parentheses.

However, is there an easier way to solve this problem?

Aemilius
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    A truth table? Or showing that a string of XOR is true iff an odd number of the variables are true, no matter how you associate them. – Arthur Oct 10 '17 at 06:59
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    It's surprising that you haven't been introduced to truth tables... – Jean Marie Oct 10 '17 at 07:02
  • I am a little bit ashamed that I haven't thought of a truth table in the first place... Thanks for your help! – Aemilius Oct 10 '17 at 07:08

2 Answers2

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Using a logical calculator and bitwise operations,

$$(55_H\oplus33_H)\oplus0F_H=66_H\oplus0F_H=69_H$$

$$55_H\oplus(33_H\oplus0F_H)=55_H\oplus3C_H=69_H$$

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We did those kind of problems last year for an exam. The teacher asked us to solve it using your approach, but we could also use truth tables for a lower score. It would be like this:xor truth table

Cristina
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