The following "definitions" of a group are taken verbatim, including spelling and punctuation, from papers of students who wrote a bit too quickly and carelessly. Criticize them.

a. A group G is a set of elements together with a binary operation * such that the following conditions are satisfied * is associative 

There exists e ∈ G such that e * x = x * e = x = identity. For every a ∈ G there exists an a' (inverse) such that a. a' = a' . a = e. b. A group is a set G such that. The operation on G is associative. there is an identity element (e) in G. a • a' = a' • a = e, for every a ∈ G, there is an a' (inverse for each element)

c. A group is a set with a binary operation such  the binary operation is defined an inverse exists an identity element exists 

d. A set G is called a group over the binary operation * such that for all a, b ∈ G Binary operation * is associative under addition there exist an element {e} such that a * e = e * a = e. Fore every element a there exists an element a' such that a * a' = a' * a = e