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Please provide an explanation! Let (A, Prove or disprove: if both A and B are dense, then so is A x B with the product

Please provide an explanation!

Let (A,

Prove or disprove: if both A and B are dense, then so is A x B with the product ordering. Prove or disprove: if both A and B are dense, then so is A x B with the lexicographic ordering

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