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(a) Find all non-empty finite sets of integers A and B with the following properties: (i) Whenever x is in A, x + 1

(a) Find all non-empty finite sets of integers A and B with the following properties: (i) Whenever x is in A, x + 1 is in B. (ii) Whenever x is in B, x2 - 4 is in A. (b) Find all positive integers a and b such that there are non-empty finite sets A and B with the property that whenever x is in A, x + a is in B, and whenever x is in B, x2 - b is in A.

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