Question $3-25$ pts

Let propositional variable $R$ be that $"$It is raining," the variable $C$ be that $"$It is cloudy," and the variable $S$ be that $"$It is sunny." Which of the following a propositional logic representation of the sentence $"$If it is raining, then it is cloudy and not sunny."?

$($a$)RC$notS

$($b$)R^{{?}^{?}}{C}^{{?}^{?}}$notS

$($c$)(RC{)}^{{?}^{?}}$notS

$($d$)R(C^{{?}^{?}}$notS$)$

$($e$)(CvvnotS)R$

Question $4-25$ pts

Consider the following FOL predicate symbols.

Student$($x$)$ represents the predicate $"x$ is a student."

Course$(x)$ represents the predicate $"x$ is a course."

Enrolled$(x,y)$ represents the predicate $"x$ is enrolled in $y.$

Which of the following is a first$-$order logic translation of the sentence "There is a course that Ayla and Bora are both enrolled in$."?$

$($a$)$ EEx Enrolled$($Bora$,x$ Enrolled$($Ayla$,x)$

$($b$)$ AAx Enrolled$($Bora$,x$ Enrolled$($Ayla$,x)$

$($c$)$ EEx Enrolled$($Bora$,x$ Enrolled$($Ayla$,x)$

$($d$)$ AAx Enrolled$($Bora$,x)vv$ Enrolled$($Ayla$,x)$

$($e$)$ EEx Course $(x{)}^{{?}^{?}}$ Enrolled $($Bora$,x$ Enrolled$($Ayla$,x)$

$($f$)$ AAx Course Ayla, $x$

$2$