Let D be the set of all students at your school, and let M(s) be a ”s is a math major”, let C(s)”s is a computer science student”, and let E(s) be ”s is an engineering student.” Express each of the following statements using quantifiers, variables, and predicates M(s), C(s) and E(s)

1) ”There is at least one student s ${\displaystyle \in D}$ such that s is a math major and s is an engineering student”
There is at least one” implies an existential statement, thus we need to use ${\displaystyle \mathrm{\exists }}$ instead.
Replace ”s is a math major” by ${\displaystyle M\left(s\right)}$, ”s is an engineering student” by ${\displaystyle E\left(s\right)}$ and ”and” by ${\displaystyle \wedge .}$
existss ${\displaystyle \in D}$ such that ${\displaystyle M\left(s\right)\wedge E\left(s\right)}$

2) ”For every student s ${\displaystyle \in D,}$ if s is a computer science student, then s is an engineering student.”
”For every” implies an universal statement, thus we need to use ${\displaystyle \mathrm{\forall }}$ instead.
Replace ”s is a computer science student” by ${\displaystyle C\left(s\right),}$ ”s is an engineering student” by ${\displaystyle E\left(s\right)}$ and ”if-then” by ${\displaystyle \to }$. ${\displaystyle \mathrm{\forall }s\in D,C\left(s\right)\to E\left(s\right)}$

3) ”For every student s ${\displaystyle \in D,}$ if s is a computer science student, then s is not an engineering student.” ”For every” implies an universal statement, thus we need to use $\mathrm{\forall }$ instead. Replace ”s is a computer science student” by ${\displaystyle C\left(s\right),}$ ”s is an engineering student” by (s), "ifthen” by ${\displaystyle \to }$ and ”not” by ~ ${\displaystyle \mathrm{\forall }s\in D,C\left(s\right)\to \sim E\left(s\right)}$

4) ”There is at least one student s ${\displaystyle \in D}$ such that s is a math major and s is a computer science student”. ”There is at least one” implies an existential statement, thus we need to use $\mathrm{\exists }$ instead. Replace ”s is a math major” by ${\displaystyle M\left(s\right),}$ ”s is a computer science student” by
C(s) and ”and” by ${\displaystyle \wedge .}$
${\displaystyle \mathrm{\exists }s\in D}$ such that ${\displaystyle M\left(s\right)\wedge C\left(s\right)}$

5) ”There is at least one student s ${\displaystyle \in D}$ such that s is a computer science student and s is an engineering student, and There is at least one student ${\displaystyle t\in D}$ such that t is a computer science student and t is an engineering student” ”There is at least one” implies an existential statement, thus we need to use $\mathrm{\exists }$ instead.
Replace ”s is a computer science student” by ${\displaystyle C\left(s\right),}$ ”s is an engineering student” by ${\displaystyle E\left(s\right),}$ and” by ${\displaystyle \wedge }$ and ”not” by ~ ${\displaystyle (\mathrm{\exists }s\in D }$ such that ${\displaystyle C\left(s\right)\wedge E\left(s\right))\wedge }$ (${\displaystyle \mathrm{\exists }t\in D}$ such that ${\displaystyle C\left(s\right)\wedge \sim E\left(s\right)}$)