Given below are two statements : Statement I: "Grandparent is a parent of…
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\(\forall g\), c grandparent \((g, c) \Leftrightarrow \exists p\) parent \((𝑔,𝑝)∧ parent (𝑝,𝑐)\)
In the light of the above statements, choose the most appropriate answer from the options given below :
- A.
Both Statement I and Statement II are correct
- B.
Both Statement I and Statement II are incorrect
- C.
Statement I is correct but Statement II is incorrect
- D.
Statement I is incorrect but Statement II is correct
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Correct answer: A
Answer: Both statements are correct.
Formalization: ∀g ∀c (grandparent(g,c) ⇔ ∃p (parent(g,p) ∧ parent(p,c))).
Explanation:
Interpretation of predicates: parent(x,y) means x is a parent of y; grandparent(x,y) means x is a grandparent of y.
Left-to-right (⇒): If grandparent(g,c) holds, then by the definition there must exist some p such that parent(g,p) and parent(p,c). This gives the existential witness p.
Right-to-left (⇐): If there exists p with parent(g,p) and parent(p,c), then g meets the definition of being a grandparent of c, so grandparent(g,c) holds.
Quantifier scope: g and c are universally quantified (the statement describes all possible pairs), while p is existentially quantified inside the equivalence to indicate the existence of an intermediate parent.
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