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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. On Z + , define ∗ by a ∗ b = | a – b |

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.

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

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

 We can observe that for a,b \in Z^+,there is a unique element | a - b |  in Z^+.

This means * carries each pair (a,b)  to a unique element a * b = | a - b | in Z^+.

Therefore,* is a binary operation.

 

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