r logic sentence is a good translation. If not,
explain why not and correct it.<br />

1.  Any apartment in London has lower rent than some apartments
    in Paris.<br />

$$
\forall {x} [{Apt}(x) \land {In}(x,{London})]
\implies \exists {y} ([{Apt}(y) \land {In}(y,{Paris})] \implies ({Rent}(x) &lt; {Rent}(y)))
$$

2.  There is exactly one apartment in Paris with rent below \$1000.<br />

$$
\exists {x} {Apt}(x) \land {In}(x,{Paris}) \land \forall{y} [{Apt}(y) \land {In}(y,{Paris}) \land ({Rent}(y) &lt; {Do