NIELIT 2017 DEC Scientist B - Section B: 43

Question

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

“None of my friends are perfect.”

• A. $\neg\:\exists\:x(p(x)\land q(x))$
• B. $\exists\:x(\neg\:p(x)\land q(x))$
• C. $\exists\:x(\neg\:p(x)\land\neg\:q(x))$
• D. $\exists\:x(p(x)\land\neg\:q(x))$

Comments

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.

Answer 1

check this

Answer 2

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.

Comments

yes you are incorrect 

https://gateoverflow.in/1538/gate2013_27

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What is p(x) and q(x) here?

Answer 3

“None of my friends are perfect.”

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

 $\sim \exists x(P(x) \wedge q(x)))$