What is that called in set theory that can be used in programming to make set B equal to set A by (1) adding to set B what set A has but set B does not have, and (2) removing from set B what set A does not have, but set B does have?
I think it's similar to the concept of a symmetric difference, not not alike.
Step (1) would be to add (A-B) to B.
Step (2) would be to subtract (B-A) from B.
I think it could be expressed like this:
B_prime = B + (A-B) - (B-A)
B_prime = B + A - B - B + A
B_prime = - B + A + A
If I call B_prime the resulting state of what was originally B, B_prime should be expressed as the differences between the sets plus the intersection of the sets, like so:
B_prime = (intersection between A and B) + (A-B)
B_prime = (intersection between A and B) + A - B
In code, B_prime would actually be the resulting state of B after the process is complete.
However, I am not able to make the steps I outlined agree with the way I think the expression should be expressed in terms of B_prime. How do I connect the steps I outlined with the way I think the result should be as expressed as B_prime.
Is there a name for the entire process I described? If there is a name for it than it is a likelihood that there is a function in any language that does exactly just that, and I wouldn't need to write my own code to do this.