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

What is the value of $$\mathop {\lim }\limits_{n \to \infty } {\left[ {1 - {1 \over n}} \right]^{2n}}?$$

Consider the following matrix $$A = \left[ {\matrix{ 2 & 3 \cr x & y \cr } } \right]\,\,$$ If the eigen values of $$A$$ are $$4$$ and $$8$$, then

The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree sequence of any graph?
$${\rm I}.$$$$\,\,\,\,\,7,6,5,4,4,3,2,1$$
$${\rm I}{\rm I}.$$$$\,\,\,\,\,6,6,6,6,3,3,2,2$$
$${\rm I}{\rm I}{\rm I}.$$$$\,\,\,\,\,7,6,6,4,4,3,2,2$$
$${\rm I}V.$$$$\,\,\,\,\,8,7,7,6,4,2,1,1$$