# Given below are two statements:Statement I: "Grandparent is a parent of one's parent".Statement II: First Order Predicate Logic (FOPL) representation of above statement is∀ g, c grandparent (g, c) ⇔ ∃ p parent (g, p) ∧ parent (p, c)In the light of the above statements, choose the most appropriate answer from the options given below:

This question was previously asked in
UGC NET Computer Science (Paper 2) 8 Oct 2022 Official Paper
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1. Both Statement I and Statement II are correct
2. Both Statement I and Statement II are incorrect
3. Statement I is correct but Statement II is incorrect
4. Statement I is incorrect but Statement II is correct

Option 1 : Both Statement I and Statement II are correct
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UGC NET Paper 1: Held on 11th Dec 2023 Shift 2
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50 Questions 100 Marks 60 Mins

## Detailed Solution

Explanation:Statement I: "Grandparent is a parent of one's parent".

Statement II: First Order Predicate Logic (FOPL) representation of above statement is

• ∀ g, c grandparent (g, c) ⇔ ∃ p parent (g, p) ∧ parent (p, c)
• Here: Statement 2 is First Order Predicate Logic (FOPL) representation of statement1
• ∃ p parent (g, p) means for at least one grandparent of parent
• parent (p, c) means parent of child
• conclusion: "Grandparent is a parent of one's parent".

FOPL is a mathematical language used to represent logical statements and relationships between entities.

• In FOPL, we use quantifiers to denote the scope of variables in a logical statement.
• The two main quantifiers are universal (∀) and existential (∃).
• In Statement II, the universal quantifier (∀) is used to represent all grandparent relationships.
• The variables g and c represent a grandparent and a grandchild, respectively.
• The FOPL representation asserts that for all grandparent (g, c) relationships, there exists a parent (p) such that p is a parent of c, and g is a parent of p.
• This representation accurately represents the grandparent relationship defined in Statement I.
• In summary, both Statement I and Statement II are true.
• Statement I provides an intuitive definition of the grandparent relationship, while Statement II provides a formal representation of the same relationship using FOPL.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Given below are two statements:Statement I: "Grandparent is a parent of one's parent".Statement II: First Order Predicate Logic (FOPL) representation of above statement is∀ g, c grandparent (g, c) ⇔ ∃ p parent (g, p) ∧ parent (p, c)In the light of the above statements, choose the most appropriate answer from the options given below:

This question was previously asked in
UGC NET Computer Science (Paper 2) 8 Oct 2022 Official Paper
View all UGC NET Papers >
1. Both Statement I and Statement II are correct
2. Both Statement I and Statement II are incorrect
3. Statement I is correct but Statement II is incorrect
4. Statement I is incorrect but Statement II is correct

Option 1 : Both Statement I and Statement II are correct
Free
UGC NET Paper 1: Held on 11th Dec 2023 Shift 2
18.4 K Users
50 Questions 100 Marks 60 Mins

## Detailed Solution

Explanation:Statement I: "Grandparent is a parent of one's parent".

Statement II: First Order Predicate Logic (FOPL) representation of above statement is

• ∀ g, c grandparent (g, c) ⇔ ∃ p parent (g, p) ∧ parent (p, c)
• Here: Statement 2 is First Order Predicate Logic (FOPL) representation of statement1
• ∃ p parent (g, p) means for at least one grandparent of parent
• parent (p, c) means parent of child
• conclusion: "Grandparent is a parent of one's parent".

FOPL is a mathematical language used to represent logical statements and relationships between entities.

• In FOPL, we use quantifiers to denote the scope of variables in a logical statement.
• The two main quantifiers are universal (∀) and existential (∃).
• In Statement II, the universal quantifier (∀) is used to represent all grandparent relationships.
• The variables g and c represent a grandparent and a grandchild, respectively.
• The FOPL representation asserts that for all grandparent (g, c) relationships, there exists a parent (p) such that p is a parent of c, and g is a parent of p.
• This representation accurately represents the grandparent relationship defined in Statement I.
• In summary, both Statement I and Statement II are true.
• Statement I provides an intuitive definition of the grandparent relationship, while Statement II provides a formal representation of the same relationship using FOPL.
user
The text passage contains two statements about the definition of a grandparent and its representation in First Order Predicate Logic (FOPL), followed by a multiple-choice question and an explanation of the correct answer.

TYPE: NO_QUESTION

However, upon closer inspection, the passage does contain a multiple-choice question asking about the correctness of the two statements. Therefore, the correct analysis is:

TYPE: SINGLE_QUESTION_WITH_ANSWER