Group A group,denoted by (G,),is a set G with a binary operation GXG>G such that -Associativity:a(boc)=(ab)oc(associative) -Existence of identity:there exists e Gs.t.VxeG,ex=x oe =x(identity) -Existence of inverse:for any x e G,there exists y Gs.t.x y=yox=e (inverse) ·A group(G,)is commutative if Vx,.y∈G,xoy=yo X. Examples:(Z,+),(2,+),(Q{0},×),(R,+),(R{0}, X) 66 Group  A group, denoted by (G, ◦), is a set G with a binary operation ◦: G×GG such that ─ Associativity: a ◦ (b ◦ c) = (a ◦ b) ◦ c (associative) ─ Existence of identity: there exists e ∈ G s.t. ∀x ∈ G, e ◦ x = x ◦ e = x (identity) ─ Existence of inverse: for any x ∈ G, there exists y ∈ G s.t. x ◦ y = y ◦ x = e (inverse)  A group (G, ◦) is commutative if ∀x, y ∈ G, x ◦ y = y ◦ x.  Examples: (Z, +), (Q, +), (Q\{0}, ×), (R, +), (R\{0}, ×)