Determine the truth value of each statement, assuming that x and y are real numbers. Justify your answer. (a) ∀x, ∃ y  xy = 0. (b) ∀x, ∃ y  xy = 1. (c) ∃ y  ∀ x, xy = 1. (d) ∀x, ∃ y  xy = x.

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