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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
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Translate ∀x∃y(x < y) in English, considering domain a...
Explanation:

Understanding the statement:
The statement ∀x∃y(x < y)="" translates="" to="" "for="" all="" real="" numbers="" x,="" there="" exists="" a="" real="" number="" y="" such="" that="" x="" is="" less="" than="" />

Breaking down the statement:
- ∀x: This symbol (∀) represents "for all" or "for every." In this case, it indicates that the following statement applies to all real numbers x.
- ∃y: This symbol (∃) represents "there exists" or "there is." It indicates that there exists a real number y that satisfies the given condition.
- (x < y):="" this="" part="" of="" the="" statement="" states="" that="" x="" is="" less="" than="" />

Explanation of option 'A':
Option 'A' correctly translates the given statement by stating that for every real number x, there exists a real number y such that x is less than y. This interpretation accurately captures the meaning of the original statement in English.
Therefore, the correct answer is option 'A': "For all real number x there exists a real number y such that x is less than y."
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Community Answer
Translate ∀x∃y(x < y) in English, considering domain a...
Statement is x is less than y. Quantifier used are for each x, there exists a y.
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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 yb)For every real number y there exists a real number x such that x is less than yc)For some real number x there exists a real number y such that x is less than yd)For each and every real number x and y such that x is less than yCorrect answer is option 'A'. Can you explain this answer?
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