Question

Translate ∀x∃y(x < y) in English, considering domain as a real number for both the variable.

(a) For all real number x there exists a real number y such that x is less than y

(b) For every real number y there exists a real number x such that x is less than y

(c) For some real number x there exists a real number y such that x is less than y

(d) For each and every  real number x and y such that x is less than y

This question was posed to me during a job interview.

Question is taken from Logics in section The Foundation: Logics and Proofs of Discrete Mathematics

Answer 1

The correct choice is (a) For all real number x there exists a real number y such that x is less than y

The best explanation: Statement is x is less than y. Quantifier used are for each x, there exists a y.