$1.$ Schematize, taking the UD to be the class of all persons, and using $$S$$ for $$ is a soprano$,$T$$ for $$ is a tenor$,$R$$ for $$ respects $,$ and $$L$$ for $$ is louder than $(10$ pts each$)$: a$.$ A tenor who is louder than any soprano is also louder than some tenor. b$.$ A tenor respects a soprano if and only if that soprano is louder than he$.$ c$.$ There are sopranos who respect only those tenors who are louder than they. $2.$ Schematize, taking the UD to be the class of all persons, and using $$P$$ for $$ is a professor$,$S$$ for $$ is a student$,$R$$ for $$ respects $,$ and $$A$$ for $$ adulates $(10$ pts each$)$: a$.$ There is someone who, although not a herself a student, respects some student who respects no professor. b$.$ Every self$-$respecting student who adulates no professor is respected by some student whom no professor respects. $3.$ With UD and vocabulary as in problem $2,$ translate the following into clear, idiomatic English $(10$ pts each$)$: a$.($$x$)[$Px $("$y$)($Sy $($$z$)($Pz $$ Ayz$)$ Ayx $)]$ b$.("$x$)[$Px $(("$y$)($Sy $$ Ryx$)($$y$)$ Axy $)]4.$ Interpreting $$H$$ as $$ helps $,$ and taking the UD to be the class of persons, render the following into clear idiomatic English $(10$ pts each$)$: a$.("$x$)[($$y$)$ Hyx $($$y$)$ Hxy $]$ b$.("$x$)[$Hxx $("$y$)($~Hyy $$ ~Hy