 Solution

ID: past-exam-of-the-computer-science-course-of-the-university-of-oxford/2015/logic-and-proof/3/a/c/solution

The same person

y

must both love

x

and be loved by

x

\forall x [(\exists y (L (y, x) \land L (x, y))) \to H (x)] .

Equivalently, use

\forall x \forall y [(L (y, x) \land L (x, y)) \to H (x)]

. There is no restriction that

x

and

y

be distinct; this matters when the later ground resolution proof considers Lucy loving herself.

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