Q46.Marks: +2.0UGC NET Paper 2: Computer Science 8th Oct 2022
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:
1.Both Statement I and Statement II are correct✓ 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
Solution
Correct answer is Option 1
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.