Suppose the predicate $F(x, y, t)$ is used to represent the statement that person $x$ can fool person $y$ at time $t$. which one of the statements below expresses best the meaning of the formula $\forall x \exists y \exists(\neg F(x,y,t))$?
(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
The formula $\forall x \exists y \exists (\neg F(x,y,t))$ says that for every person $x$, there exists a person $y$, and there exists a time $t$, such that $x$ cannot fool $y$ at time $t$ i.e., No person can fool everyone all the time. So option (B) is correct.
Suppose the predicate $F(x, y, t)$ is used to represent the statement that person $x$ can fool person $y$ at time $t$. which one of the statements below expresses best the meaning of the formula $\forall x \exists y \exists(\neg F(x,y,t))$?
(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
The formula $\forall x \exists y \exists (\neg F(x,y,t))$ says that for every person $x$, there exists a person $y$, and there exists a time $t$, such that $x$ cannot fool $y$ at time $t$ i.e., No person can fool everyone all the time. So option (B) is correct.
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