Q.1 Determine whether or not each of the definition of ∗ given below gives a binary
operation. In the event that ∗ is not a binary operation, give justification for this.

(i) On Z^+ , define ∗ by a * b = a - b

Answers (1)

(i) On Z^+ , define ∗ by a * b = a - b

 It is not a binary operation as the image of (1,2) under * is 1\ast 2=1-2 =-1 \notin Z^{+}.

 

                                                                                                                   

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