$1)$ Represent the following sentences in first$-$order logic, using a consistent vocabulary $($which you must define$)$ a$)$ Some students took French in spring $2001.$ b$)$ Every student who takes French passes it$.$ c$)$ Every person who buys a policy is smart. d$)$ No person buys an expensive policy.Represent the following sentences in first$-$order logic, using the predicates given here.

Take $(x,y,z)$ means $"x$ took course $y$ in year $z",$ e$.$g$.$ Take$($Tomal$,$ CSE$440,2020)$

Pass $(x,y,z)$ means $"x$ passed course $y$ in year $z",$ e$.$g$.$ Pass$($Zerin$,$ CSE$373,2021)$

Hard$(x)$ means "Course $x$ is hard", e$.$g$.$ Hard$($CSE$215)$

Now write the following statements in First order logic.

a$)$ Abhijit took CSE$171$ in $2020$ and passed it$.$

b$)$ Every student who takes CSE$115($in any year$)$ passes it$.$

c$)$ Some students took CSE$229$ in $2021$

d$)$ Shurra passed every course that she took in $2020.$