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| − | Suppose the predicate F(x, y, t) is used to represent the statement that person x | + | 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 | + | can fool person $y$ at time $t$. which one of the statements below expresses best |
| − | the meaning of the formula | + | the meaning of the formula $\forall x \exists y \exists(\neg F(x,y,t))$? |
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| − | + | ||
| − | + | (A) Everyone can fool some person at some time | |
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| − | + | ''' (B) No one can fool everyone all the time''' | |
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| − | + | (C) Everyone cannot fool some person all the time | |
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| − | + | (D) No one can fool some person at some time | |
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| − | + | ==={{Template:Author|Happy Mittal|{{mittalweb}} }}=== | |
| − | 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>(B)</b> is correct. | + | |
| + | 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>(B)</b> is correct. | ||
{{Template:FBD}} | {{Template:FBD}} | ||
[[Category: GATE2010]] | [[Category: GATE2010]] | ||
| − | [[Category: | + | [[Category: Mathematical Logic questions from GATE]] |
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 ∀x∃y∃(¬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
</p>
Sol : The formula ∀x∃y∃(¬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.
GATECSE