D. Determine whether or not each of the following definitions of * given below does give a binary operation on the given set. In the event that * is not a binary operation, state whether condition 1...

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Extracted text: D. Determine whether or not each of the following definitions of * given below does give a binary operation on the given set. In the event that * is not a binary operation, state whether condition 1 (well definedness, condition 2 (closure property), or both of these conditions are violated. 1. On Z*, define * by a * b = a/b 2. On R- {0}, define * by a *b = ab E. For each binary operation * defined on a set below, say whether or not * gives a group structure on the set. If no group results, give the axiom that does not hold. 1. (R* , * ) where * is defined by a * b = ab 2. (Z, * ) where * is define by a * b = a - b. F. Let a e G where G is a group. What shall you show to prove that a= q?