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Which one is the correct translation of the following statement into mathematical logic?

“None of my friends are perfect.”

  1. $\neg\:\exists\:x(p(x)\land q(x))$
  2. $\exists\:x(\neg\:p(x)\land q(x))$
  3. $\exists\:x(\neg\:p(x)\land\neg\:q(x))$
  4. $\exists\:x(p(x)\land\neg\:q(x))$
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statement.
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Sorry, updated now
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None of my friends are perfect == Not ( one of my friend is perfect) = Not ( ∃x(p(x)∧q(x)) ) = ¬ (∃x(p(x)∧¬q(x)))

A will be answer
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Read it as “All of my friends are not perfect”.

For all x, is x is my friend then he/she is not perfect.

Solving implication will give us our result.
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3 Answers

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check this

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let write a logic for "All my friends are perfect"

$\vee x(q(x)\rightarrow p(x))$

take negation of above "none of my friends are perfect"

$\sim(\vee x(q(x)\rightarrow p(x)))$

$\sim\vee x (\sim q(x)\vee p(x))))$

$Ǝx(q(x)\wedge \sim p(x))$

 

Correct me if I am wrong.

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What is p(x) and q(x) here?
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“None of my friends are perfect.”

It says that It is a false that i have friend and he is perfect 

 $\sim \exists x(P(x) \wedge q(x)))$

Answer:

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