Let L(x, y) be the statement “x loves y” where the domain for both x and y…
2024
Let L(x, y) be the statement “x loves y” where the domain for both x and y consists of all people in the world. Use quantifiers to express “Joy is loved by everyone”.
- A.
∀x L(x, Joy)
- B.
∀y L(Joy, y)
- C.
∃y∀x L(x, y)
- D.
∃x~L(Joy, x)
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Show answer & explanation
Correct answer: A
Correct formula: ∀x L(x, Joy)
Explanation: This says that for every person x, x loves Joy, which exactly matches the English sentence “Joy is loved by everyone.”
Key insight: Place Joy as the object in the predicate and quantify universally over all people as the subject.
Common incorrect formulas and why they are wrong:
∀y L(Joy, y) — This means Joy loves everyone (Joy is the subject), not that everyone loves Joy.
∃y∀x L(x, y) — This says there exists someone who is loved by everyone, but it does not specify that this someone is Joy.
∃x ¬L(Joy, x) — This states there is someone Joy does not love, which is unrelated and almost the opposite kind of claim.
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