Q1 of 107 Page 24

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 that On Z+, define ∗ by a ∗ b = a – b

It is not a binary operation as the image of (1, 2) under * is


1 * 2 = 1 – 2 = -1 Z+.


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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.

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