Symbolisation II

Are the following analyses correct? Why?

1. There is exactly one frog:
   $\exists$x$\exists$y[[x is a frog $\wedge$ y is a frog] $\wedge$ x = y]
2. There are at least two frogs:
   $\exists$x$\exists$y[x is a frog $\wedge$ y is a frog]
3. There are no frogs:
   $\forall$x$\forall$y[[x is a frog $\wedge$ y is a frog] $\rightarrow$ $\neg$ x = y]