Let (G, ∗) be an algebraic structure. Recall that (G, ∗) is a group if and only if G satisfies 3 properties: • associativity: for every a, b, c ∈ G, a ∗ (b ∗ c) = (a ∗ b) ∗ c. • existence of an identity: there exists an element e ∈ G such that for every a ∈ G, e∗a = a∗e = a. • existence of inverses: for every a ∈ G, there exists an element b ∈ G, such that a ∗ b = b ∗ a = e. State what it mean to say that (G, ∗) is not a group