Let ∘ be a binary operation on a set S. The cancellation laws are said to hold if, for all a, b, and c in S,
(i) if a ∘ b = a ∘ c, then b = c,
(ii) if b ∘ a = c ∘ a, then b = c.
It can be shown, for example, that in a group the cancellation laws hold.
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