SOLVED: Give a recursive definition of each of these sets of ordered pairs of positive integers. (Hint: plot the points of the set in the plane and look for lines containing points in the set)1. S = (a,6) | a ∈ ℤ⁺ and a divides 62. S = (a,6) | a ∈ ℤ⁺, b ∈ ℤ⁺, and a b is odd3. S = (a,6) | a ∈ ℤ⁺, b ∈ ℤ⁺, and 3 divides a divides 6a) (1,2) ∈ S, (2,1) ∈ S, and if (a,b) ∈ S, then (a 2,6) ∈ S, (0,6 2) ∈ S, and (a 1,6 1) ∈ S(1,2) ∈ S, (2,1) ∈ S, and i
SOLVED: Give a recursive definition of each of these sets of ordered p…
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SOLVED:Give a recursive definition of each of these sets of ordered pairs of positive integers. Use structural induction to prove that the recursive definition you found is correct. [Hint: To find a recursive definition, plot the points in the set in the plane and look for patterns.] a) S={(a, b) | a ∈𝐙^ , b ∈𝐙^ , and a b is even } b) S={(a, b) | a ∈𝐙^ , b ∈𝐙^ , and a or b is odd } c) S={(a, b) | a ∈𝐙^ , b ∈𝐙^ , a b is odd, and 3 | b}
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