Question

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 Ñ Z+ , and a | b}2. S={(a, b) I a E Z+, b Ñ Z+ , and 3 | a + b} 3. S={(a, b) | a Ñ Z+ , b Ñ 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) Ñ Sand if (a, b) Ñ S then (a + 3, b) Ñ s, (a, b + 3) Ñ s, (a+1, b + 2) ES and (a + 2, b + 1) Ñ s c) (1,1) Ñ Sand if (a, a) Ñ Sthen (a + 1, a + 1) Ñ S and if (a, b) Ñ S, then (a, b + a) Ñ s

Answer 1

Answer:

1. s=gfcgj sdgc

gzgixxhcxc

vxtuixzdfhvxxgjknn

jfhujhgcxvjkmvcghj

mvhuiknbb5542698755

8423675369

8823