What is the logical translation of the following statement? “None of my…
20132013
What is the logical translation of the following statement?
“None of my friends are perfect.”
Answer: D. \(¬∃ x (F (x)∧ P(x))\) — Correct logical form: ¬∃x (F(x) ∧ P(x)) — there is no x who is both a friend and perfect. Equivalent universal form: ∀x (F(x) → ¬P(x)). For every x, if x is…
- A.
\(∃x (F (x)∧ ¬P(x)) \) - B.
\(∃ x (¬ F (x)∧ P(x))\) - C.
\(∃x (¬F (x)∧¬P(x))\) - D.
\(¬∃ x (F (x)∧ P(x))\)
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Correct answer: D
Correct logical form: ¬∃x (F(x) ∧ P(x)) — there is no x who is both a friend and perfect.
Equivalent universal form: ∀x (F(x) → ¬P(x)). For every x, if x is my friend then x is not perfect.
Why they are equivalent: ¬∃x (F(x) ∧ P(x)) is equivalent to ∀x ¬(F(x) ∧ P(x)), and ¬(F(x) ∧ P(x)) is equivalent to (F(x) → ¬P(x)).
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