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min a b + max a b = a + b
GCD a b * LCD a b = a * b
μ(A ∩ B) + μ(A ∪ B) = μ(A) + μ(B)

What is the general name for these correspondences? And what are other examples?

• Positive (incl. 0) numbers, ordered by subtractability, ≤.
• Integers, ordered by divisibility, |.
• Measurable sets / probabilities, ordered by inclusion / entailment, ⊆.

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