1. On R, define ∗ by a ∗ b = ab2
2. On Z+, define ∗ by a ∗ b = | a – b |

(iii) On R, characterize ∗ by a ∗ b = ab2 R = { – ∞, … , – 1, 0, 1, 2,… … , ∞} Let a = 1.2 and b = 2

Accordingly, a ∗ b = ab2 = (1.2) x 22 = 4.8 ∈ R Operation * is a double procedure on R.

(iv) On Z+, characterize ∗ by a ∗ b = | a – b |

On Z+ = {1, 2,3 , 4, 5,… … .}

Let a = 2 and b = 3

In this way, a ∗ b = a b = 2 * 3 = 6 ∈ Z+ activity * is a twofold procedure on Z+