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) V In(Gwalior, India) Which one of the following is correct with respect to the above logical sentence ?

1. AIt is syntactically valid but does not express the meaning of the English sentence.
2. BIt is syntactically valid and expresses the meaning of the English sentence also.
3. CIt is syntactically invalid but expresses the meaning of the English sentence.
4. DIt is syntactically invalid and does not express the meaning of the English sentence.

Pick an option to check yourself, or open the answer below.

Show answer & explanation

Correct answer: A. It is syntactically valid but does not express the meaning of the English sentence.

Explanation

The sentence is well-formed but uses ∨; 'both' needs In(Agra, India) ∧ In(Gwalior, India).