Explanation
To identify X as the grandmother of Y, we need:
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Gender: X must be female (ψ or ϵ relative to someone).
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Generation Gap: There must be exactly two generations between X and Y (e.g., X→Parent→Y).
Let's evaluate the options:
Option (a): L # Y"data−index−in−node="12">X \ \epsilon \ Z \ \psi \ K \ \ L # Y
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X ϵ Z⟹X is sister of Z.
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Z ψ K⟹Z is mother of K.
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L⟹K"data−index−in−node="0">K \ \ L⟹K is father of L.
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L # Y⟹L is brother of Y.
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Analysis: X is the sister of Y's grandmother (Z). So, X is a great-aunt, not the real grandmother.
Option (b): X # L"data−index−in−node="12">Y \ \psi \ K \ \ X # L
Option (c): K ψ X ϵ Z"data−index−in−node="12">Y \ \# \ L \ \ K ψ X ϵ Z
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K⟹L"data−index−in−node="0">L \ \ K⟹L is father of K.
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K ψ X⟹K is mother of X.
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Analysis: Again, Y and L are in older generations than X. This would make Y the uncle of X.
Option (d): Y"data−index−in−node="12">K \ \# \ X \ \psi \ Z \ \# \ L \ \ Y
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X ψ Z⟹X is mother of Z.
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Z # L⟹Z is brother of L.
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Y⟹L"data−index−in−node="0">L \ \ Y⟹L is father of Y.
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Analysis:
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Result: Since X is the mother of Y's father (L), X is definitely the grandmother of Y.
Final Answer:
Option (d) correctly establishes that X is the mother of Y's father, making her the real grandmother.
Correct Option: (d) Y"data−index−in−node="20">K \ \# \ X \ \psi \ Z \ \# \ L \ \ Y
