text: # 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.
explanation: The document contains a question and its answer. The question is a multiple-choice question about the correctness of two statements related to the definition of a grandparent and its representation in First Order Predicate Logic (FOPL). The answer provided is that both statements are correct.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # 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.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a question and its answer. The question is a multiple-choice question about the correctness of two statements related to the definition of a grandparent and its representation in First Order Predicate Logic (FOPL). The answer provided is that both statements are correct.
  
  Label: question-and-answer