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∃t(¬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
link to the question https://www.geeksforgeeks.org/gate-gate-cs-2010-question-30/
Why answer is not D and what should be the expression for D to be correct ?
After applying demorgan result will be ¬{∃x∀y∀t(F(x, y,t))}
So I should take negation of whole statement or negation of just ∃x which is (¬∃x)∀y∀t(F(x,y,t))
The statement which I am getting is ¬(there exist some x who can fool all y at all time t)
so is it equal to
"there doesn't exist anyone who can fool all y at all time t" which is (¬∃x)∀y∀t(F(x,y,t))
Or
"No one can fool some person at some time"?
