Multiple choice

What is the logical translation of the following statement?

“None of my friends is perfect.”

  1. $∃x(F (x)∧ ¬P(x))$
  2. $∃ x(¬ F (x)∧ P(x))$
  3. $ ∃x(¬F (x)∧¬P(x))$
  4. $ ¬∃ x(F (x)∧ P(x))$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

“None of my friends is perfect” $ \begin{aligned} \qquad & = \forall x(F (x)∧ \neg P(x)) \\ & = \forall x( \neg F (x)∧ \neg P(x)) \\ & = ¬∃ x(F (x)∧ P(x)) \end{aligned} $

Keep practicing — related questions