I was looking for a way to do a BITOR() with an Oracle database and came across a suggestion to just use BITAND() instead, replacing BITOR(a,b) with a + b - BITAND(a,b).

I tested it by hand a few times and verified it seems to work for all binary numbers I could think of, but I can't think out quick mathematical proof of why this is correct.
Could somebody enlighten me?

oracle-database binary computer-science theory proofs
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