Mathematics, 07.07.2020 17:01 andrespeerman
Give a recursive definition of each of these sets of ordered pairs of positive integers. (Hint: plot the points in the set in the plane and look for lines containing points in the set. 1. S={(a, b) I a E Z+, b Γ Z+ , and a | b}2. S={(a, b) I a E Z+, b Γ Z+ , and 3 | a + b} 3. S={(a, b) | a Γ Z+ , b Γ Z+ , and a + b is odd) a) (1,2) S, (2, 1) E S and if (a, b) S then (a + 2, b) E S, (a, b + 2) E S and (a + 1, b + 1) E S b) (1,2) es, (2, 1) Γ Sand if (a, b) Γ S then (a + 3, b) Γ s, (a, b + 3) Γ s, (a+1, b + 2) ES and (a + 2, b + 1) Γ s c) (1,1) Γ Sand if (a, a) Γ Sthen (a + 1, a + 1) Γ S and if (a, b) Γ S, then (a, b + a) Γ s
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Give a recursive definition of each of these sets of ordered pairs of positive integers. (Hint: plot...
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