Question

Suppose the predicate F(x, y, t) is used to represent the statement that person x can fool person y at time 1. Which one of the statements below expresses best the meaning of the formula $\forall x\exists y\exists t(\neg ,F(x,y,t\left)\right)?$

• A. Everyone can fool some person at some time
• B. No one can fool everyone all the time
• C. Everyone cannot fool some person all the time
• D. No one can fool some person at some time

Answer 1

The correct option is B No one can fool everyone all the time

$\forall x\exists y\exists t\neg F(x,y,t)$
$\equiv \neg \exists x\forall y\forall tF(x,y,t)$
$\equiv$ It is not true that (someone can fool all people at all time)
$\equiv$ no one can fool everyone all the time