cancellation laws

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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 ab=ac, then b=c,(ii) if ba=ca, then b=c.It can be shown, for example, that in a group the cancellation laws hold.

(i) if ab=ac, then b=c,

(ii) if ba=ca, then b=c.

Subjects: Mathematics.

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