UGC NET CSE | July 2018 | Part 2 | Question: 77

Question

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) $\vee$ 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

Answer 1

Given that "Agra and Gwalior are both in India"

representation :-  In(x,y) means x is in India

In(Agra,India) ----(1)

In(Gwalior,India) ---(2)

According to the english statement, In(Agra,India) is should be true, In(Gwalior,India) is should be true

therefore use Conjunction as Connector ===> In(Agra,India) ^ In(Gwalior,India).

but given that In(Agra,India) ⋁ In(Gwalior,India) ====> syntactically correct but not represent the given enlish statement.

 

option :- a is correct

Answer 2

I think the correct answer is A

because the given predicate                In(Agra, India) ∨ In(Gwalior, India)   represent that at least one of Agra and Gwalior in INDIA

 

so the correct representation of the given  English sentence is 

In(Agra, India) $\Lambda$ In(Gwalior, India)

Answer 3

The given logical sentence is syntactically valid and expresses the meaning of the English sentence. In first-order logic, the IN(x, y) predicate represents the relationship between two objects, x and y, such that x is in y. The sentence "In(Agra, India) In(Gwalior, India)" uses the IN predicate to state that Agra is in India and Gwalior is in India, which accurately reflects the meaning of the English sentence "Agra and Gwalior are both in India." Therefore, the correct answer is "It is syntactically valid and expresses the meaning of the English sentence also."