Translate into English: ∀x ∃y (x < y), where the domain of both variables is the real numbers.

1. AFor all real numbers x, there exists a real number y such that x is less than y
2. BFor every real numbers y, there exists a real number x such that x is less than y
3. CFor some real numbers x, there exists a real number y such that x is less than y
4. DFor each and every real numbers x and y, x is less than y

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Show answer & explanation

Correct answer: A. For all real numbers x, there exists a real number y such that x is less than y

Explanation

∀x ∃y (x < y): for every real x there is some real y bigger than it. The order of quantifiers matters: ∃y ∀x would claim one y bigger than every x.