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Recall that a subset A (of N, Z, Q) is called downward closed when x ∈...

Recall that a subset A (of N, Z, Q) is called downward closed when x ∈ A and y < x implies y ∈ A. Suppose that A is a downward closed subset of Z, and consider the subsets

B = {x + 1 ∈ Z | (∃y ∈ A).x2 ≤ y} C = {x − 1 ∈ Z | (∃y ∈ A).x < y2 }

For each of B, C, determine whether it is downward closed in Z. Explain why , Thanks

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