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What is the logical translation of the following statement?

"None of my friends are 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))$
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option d is correct

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Answer (D)

"None of my friends are perfect."

Its negation is atleast one of my friends is perfect  read the negation again and think

atleast one of my friends is perfect

∃x(F(x)∧P(x))

we use ∧ because I want to test my friends and true value should come from them not from outside people

if we used implication we will get true value for a person who is not even my friend and ∃x to be true only needs one true value.

now negate ∃x(F(x)∧P(x))

=> ¬∃x(F(x)∧P(x))

Answer:

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