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Check the following table:

a b c a+b+c a^b^c

0 0 0 0 0 =

0 0 1 1 1 =

0 1 0 1 1 =

0 1 1 1 0

1 0 0 1 1 =

1 0 1 1 0

1 1 0 1 0

1 1 1 1 1 =

So they are equal if the number of ones between a, b, and c is zero or an odd number.

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