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1. The set of integers that pass the condition that their square is a natural number. Well, every integer, when you square it, gives you a non-negative integer, so a natural number. Thus \(A = \Z = \{\ldots, -2, -1, 0, 1, 2, 3, \ldots\}\text{.}\)

2. Here we are looking for the set of all \(x^2\)s where \(x\) is a natural number. So this set is simply the set of perfect squares. \(B = \{0, 1, 4, 9, 16, \ldots\}\text{.}\)

   Another way we could have written this set, using more strict set builder notation, would be as \(B = \{x \in \N \st x = n^2 \text{ for some } n \in \N\}\text{.}\)