Q. 1 D4.9( 10 Votes )

# 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|

It is given On Z+, define by a b = | a – b|

We can see that for each a, b ϵ Z+, there is a unique element |a – b| in Z+.

* carries each pair (a, b) to a unique element a * b = |a – b| in Z+.

Therefore, * is a binary operation.

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