Question 77
77. 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 ?
Answer : (1) It is syntactically valid but does not express the meaning of the 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 ?
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| UGC NET CS 2018 July - II Question 76 | UGC NET CS 2018 July - II Question 78 |
Predicate In(Agra, India) means Agra is in india
Predicate In(Gwalior, India) means Gwalior is in india
According to the given english statement "Agra and Gwalior are both in India", both Predicate "In(Agra,India)" and "In(Gwalior,India)" should be true
Therefore use of conjunction as connector requires between both predicates "In(Agra, India) ∧ In(Gwalior, India)".
But given that In(Agra, India) ∨ In(Gwalior, India), in this it uses connector "∨". So, the entire gives the meaning of Either Agra is in india or Gwalior is in india.
So, Logic is not equivalent for given English sentence and given First-Order Logic.
Given predicate "In(Agra, India) ∨ In(Gwalior, India)" is syntactically correct but not represent the given english statement.
So, option 1 is correct answer