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Let P be the statement, “For all A ⊆ Z with |A| = ∞ there exists...

Let P be the statement, “For all A ⊆ Z with |A| = ∞ there exists B ⊆ Z with |B| = ∞ such that |A ∩ B| < ∞.” Write out the negation ∼ P. Which of P or ∼ P is true, and why?

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