Determine whether the binary operation * gives a group structure on the given set if. if no group results, give thr firs
Posted: Sat Feb 26, 2022 10:59 am
Determine whether the binary operation * gives a group structure on the given set if. if no group results, give thr first axiom in the order g1, g2, g3 from Definition 2.1 that does not hold.
2.26 Table b * a b a a b b b
2.1 Definition A group (G, *) is a set G, closed under a binary operation *, such that the following axioms are satisfied: 5: For all a, b, c E G, we have (a*b) *c = a* (b*c). associativity of * G: There is an element e in G such that for all x e G, e*x = x*e = x. identity element e for * 5: Corresponding to each a € G, there is an element d' in G such that a*d' = d *a= e. inverse d' of a
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2.1 Definition A group (G, *) is a set G, closed under a binary operation *, such that the following axioms are satisfied: 5: For all a, b, c E G, we have (a*b) *c = a* (b*c). associativity of * G: There is an element e in G such that for all x e G, e*x = x*e = x. identity element e for * 5: Corresponding to each a € G, there is an element d' in G such that a*d' = d *a= e. inverse d' of a