Choose the best symbolic translation for each statement given in natural language below. Use the indicated predicate symbols and individual constants to determine the best translation.

Given Statement: Some books are bestsellers.

Key of Predicate Symbols and Individual Constants: B $=$ is a book

S $=$ is a bestseller

Which expression is the best translation of the given statement above into predicate logic?

$($y$)($Sy $$ By$)$

$($y$)($By $$ Sy$)$

$($y$)($By $$ Sy$)$

$($y$)($By $$ Sy$)$

Given Statement: Some of your classmates will not pass the exam.

Key of Predicate Symbols and Individual Constants: C $=$ is your classmate

P $=$ will pass the exam

Which expression is the best translation of the given statement above into predicate logic?

$($y$)$~$($Cy $$ Py$)$

$($y$)($Cy $$ ~Py$)$

~$($y$)($Cy $$ Py$)$

$($y$)($Cy $$ ~Py$)$

Given Statement: Some things should not be repeated.

Key of Predicate Symbols and Individual Constants: R $=$ should be repeated

Which expression is the best translation of the given statement above into predicate logic?

$($z$)$Rz

$($R$)$~z

$($z$)$~Rz

~$($z$)$Rz

Given Statement: Several students passed the exam.

Key of Predicate Symbols and Individual Constants: S $=$ is a student

P $=$ passed the exam

Which expression is the best translation of the given statement above into predicate logic?

$($z$)($Pz $$ Sz$)$

$($z$)($Sz $$ Pz$)$

$($z$)($y$)($Sz $$ Py$)$

$($z$)($Sz $$ Pz$)$

Given Statement: Several people in the class passed the exam, but Robert did not pass the exam.

Key of Predicate Symbols and Individual Constants: C $=$ is a person in the class

P $=$ passed the exam

r $=$ Robert

Which expression is the best translation of the given statement above into predicate logic?

$($x$)($Cx $$ Px$)$ ~$($r$)($Cr $$ Pr$)$

$($x$)($Cx $$ Px$)$ ~$($x$)($Cx $$ Px$)$

$($x$)($Cx $$ Px$)$ ~Pr

$($r$)($Cr $$ Pr$)$ ~Pr