(a AND b) OR (a AND c) OR (b)
Since "OR b" is there, the "(a AND b)" can be dropped, since it will only be true when b is. This yeilds: (a AND c) OR b, but I have no idea how you would do that programmatically; perhaps build an n-dimensional truth table (where n is the number of variables) and come up with an algorithm to efficiently render that back into boolean terms.
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