Answer
a) $\exists x P(x)$
$\exists x (P(x) \land A(x))$
b)$\forall x Q(x)$
$\forall x (A(x) \rightarrow Q(x))$
c) $\exists x(\neg R(x))$
$\exists x (A(x) \land \neg R(x))$
d) $\exists x (S(x))$
$\exists x (A(x) \land S(x))$
e) $\neg ( \exists x T(x))$
$\neg ( \exists x (T(x)\land A(x)))$
Work Step by Step
a) There exists a person in your class that can speak hindi.
$$\exists x P(x)$$
Let P(x) be "x speaks hindi" and A(x) be " x is in your class".
$$\exists x (P(x) \land A(x))$$
b) Everyone means $\forall x$ and if x is in your class then x has to be friendly.
$$\forall x Q(x)$$
Let Q(x) be "x is friendly" and A(x) is " x is in your class".
$$\forall x (A(x) \rightarrow Q(x))$$
c) There is a person means $\exists x$ and x has to be in your class and cannot be born in california.
$$\exists x(\neg R(x))$$
Let R(x) be "x is born in california" and A(x) be "x is in your class".
$$\exists x (A(x) \land \neg R(x))$$
d) There is a student means $\exists x$ and x has to be in your class and has to have been in a movie.
$$\exists x (S(x))$$
Let S(x) be "x has been in a movie" and A(x) be "x is in your class".
$$\exists x (A(x) \land S(x))$$
e) No student means $\neg (\exists x)$ and x has to be in your class and has to have taken a course in logic programming.
$$\neg ( \exists x T(x))$$
Let T(x) be "x has taken a course in logic programming" and A(x) be " x is in your class".
$$\neg ( \exists x (T(x)\land A(x)))$$
