Let L={(a, b)|a, b∈Z,(a−b) mod 4 = 0}. We want to program a robot that can get to each point (x, y)∈L starting at (0,0). (a)Give an inductive definition of L. This will describe the steps you want the robot to take to get to points in L starting at (0,0). Let L′ be the set obtained by your inductive definition. (b)Prove inductively that L′⊆L, i.e., every point that the robot can get to is in L. (c)Prove that L⊆L′, i.e., the robot can get to every point in L. To prove this, you need to give the path the robot would take to get to every point in L from (0,0), following the steps defined by your inductive rules.

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