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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. (i) On Z+, defined ∗ by a∗b=a−b (ii) On Z+, defined ∗ by a∗b=ab (iii) On R, defined ∗ by a∗b=ab2 (iv) On Z+, defined a∗b=|a−b| (v) On Z+, defined ∗ by a∗b=a |
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Answer» 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. (ii) On Z+, defined ∗ by a∗b=ab (iii) On R, defined ∗ by a∗b=ab2 (iv) On Z+, defined a∗b=|a−b| (v) On Z+, defined ∗ by a∗b=a |
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