You are given the lexicon:

Let \(\sysm{G}\) be an abbreviation for \(\sysm{(S\fs(S\bs NP))}\)

\[\begin{align} \textit{donkey} &:=& \sysm{N} &:& \sysm{\lam x.donkey'x} &::& et\\ \textit{student}&:=& \sysm{N} &:& \sysm{\lam x.student'x} &::& et\\ \textit{John} &:=& \sysm{S\fs(S\bs NP)} &:& \sysm{\lam p.p\cnct{}john'} &::& ett\\ \quad \nonumber\\ \textit{sleeps} &:=& \sysm{S\bs NP} &:& \sysm{\lam x.sleeps'x} &::& et\\ \textit{walk(s)} &:=& \sysm{S\bs NP} &:& \sysm{\lam x.walk'x} &::& et\\ \quad \nonumber\\ \textit{lazy} &:=& \sysm{N\fs N} &:& \sysm{\lam p\lam x.p'x \land lazy'x} &::& et(et)\\ \quad \nonumber\\ \textit{slowly} &:=& \sysm{S\bs NP \bs (S\bs NP)} &:& \sysm{\lam p\lam x.slowly'px} &::& et(et)\\ \quad \nonumber\\ \textit{and} &:=& \sysm{G\bs G\fs G} &:& \sysm{\lam p\lam q\lam r.pr \land qr} &::& ett(ett(ett))\\ \quad \nonumber\\ \textit{every} &:=& \sysm{S\fs(S\bs NP)\fs N} &:& \sysm{\lam{p}\lam{q}\forall x.px\to qx} &::& et(ett)\\ \textit{a} &:=& \sysm{S\fs(S\bs NP)\fs N} &:& \sysm{\lam{p}\lam{q}\exists x.px\land qx} &::& et(et t) \end{align}\]

Provide the lexical entries for the undefined expressions to derive the meanings of the following sentences. Your definitions need to be like in the provided lexicon.

1. Every donkey admires John.
2. A donkey who admires John sleeps.
3. If John sleeps, every donkey sleeps.