 Solution

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

Lucy's happiness is a single antecedent, while the conclusion applies to everyone:

H (ℓ) \to \forall x M (x) .

Since

x

does not occur in the antecedent, this is equivalent to

\forall x [H (ℓ) \to M (x)]

. The universal quantifier does not assert that everyone is happy; it is the merriness conclusion that is universal.

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