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Now define the following sequence of operations:

1) Complement each digit in A to get a binary string A'

2) A'' = A' + 1 (here + is taken to mean binary addition rather than the boolean OR)

3) Complement each digit in A'' to get a new binary string A'''

4) A'''' = A''' + 1 (here + is taken to mean binary addition rather than the boolean OR)

Prove that for all A, A'''' = A

I appreciate all the help.

BiP