Math Problem Statement
Let S be a set. Prove that the law of composition defined by ab=a for all a and b in S is associative. For which sets does this law ha identity?
Solution
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Math Problem Analysis
Mathematical Concepts
Abstract Algebra
Binary Operations
Associativity
Identity Element
Formulas
(a * b) * c = a * (b * c)
a * e = a
e * a = a
Theorems
Associative Property
Identity Element Condition
Suitable Grade Level
College-Level Abstract Algebra
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