Originally Posted by Merriam-Webster: Is It 'Could' or 'Couldn't Care Less'?
We define could care less and couldn’t care less on the same page, with the single definition “used to indicate that one is not at all concerned about or interested in something.” We do not put these seemingly disparate idioms on the same page in order to save space, or so that we might cause you pain. We do it because one is simply a variant of the other, and they are used in a synonymous manner.
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Correct Usage: Either
[...] if you are the kind of person who cries out against this abomination we must warn you that people who go through life expecting informal variant idioms in English to behave logically are setting themselves up for a lifetime of hurt.