Consider the following English sentence: "Agra and Gwalior are both in India".…
2018
Consider the following English sentence:
"Agra and Gwalior are both in India".
A student has written a logical sentence for the above English sentence in First-Order Logic using predicate IN(x, y), which means x is in y, as follows.
In(Agra, India) ∨ In(Gwalior, India)
Which one of the following is correct with respect to the above logical sentence?
- A.
It is syntactically valid but does not express the meaning of the English sentence
- B.
It is syntactically valid and expresses the meaning of the English sentence also
- C.
It is syntactically invalid but expresses the meaning of the English sentence
- D.
It is syntactically invalid and does not express the meaning of the English sentence
Attempted by 140 students.
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Correct answer: A
Answer: The given formula In(Agra, India) ∨ In(Gwalior, India) is syntactically valid but does not capture the English meaning.
Syntactic note: The expression is well-formed if Agra, Gwalior, and India are treated as constant terms and IN is a binary predicate.
Semantic difference: The disjunction ∨ means "at least one of the two is in India." The English phrase "both ... are in India" requires both facts to be true simultaneously, which is a conjunction.
Correct logical form for the intended meaning: In(Agra, India) ∧ In(Gwalior, India)
Alternative remark: If you intended to say "At least one of Agra or Gwalior is in India," then the original disjunction is correct. Always match connectives to the English quantifier words: "both" → ∧, "either/at least one" → ∨.
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