Using Quantifiers to express "At least two" I have been stumped trying to solve problem **e**. I am confused as how to state "At least two students..." using quantifiers! I know if it were ONE student it would be: ∃x,y(Q(x,Jeopardy)). And all students would be:∀x,y(Q(x,Jeopardy)) So how can I expand on this? ![](

Suppose $P(x)$ denotes the predicate that $x$ has been on _Jeopardy_.

One can assert $\exists x,y$ s.t. $P(x) \land P(y) \land x\
eq y$.