Consider the following English sentence: “Agra and Gwalior are b
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.
Please scroll down to see the correct answer and solution guide.
Right Answer is: A
SOLUTION
Given statement is “Agra and Gwalior are both in India”.
Predicate In(x, y) means x is in y.
So,
1) In(Agra, India) – It represents Agra is in India.
2) In(Gwalior, India) – It represents Gwalior is in India.
Given predicate logic means
In(Agra, India) ∨ In(Gwalior, India) : It represents Agra is in India or Gwalior is in India.
It is not representing that both Agra and Gwalior are in India.
So, we can say that It is syntactically valid but does not express the meaning of the English sentence.