Answer
a) $\exists$xH(x)
b) $\forall$xS(x)
c) $\exists$xV(x,'Alaska') $\land$ $\neg$V(x,'Hawai')
d) $\forall$x$\exists$yL(x,y)
e) $\exists$x$\exists$y$\forall$z(O(y,z)$\rightarrow$T(x,z))
f) $\exists$x$\exists$y(G(x,t) $\land$ G(y,t))
g) $\forall$x$\exists$y$\exists$z(C(x,y,z))
Work Step by Step
The domain x of the problems is all the students in the class.
a) $\exists$xH(x), where H(x) is "x can speak Hindi".
b) $\forall$xS(x), where S(x) is "x play a sport".
c) $\exists$xV(x,'Alaska') $\land$ $\neg$V(x,'Hawai'), where V(x, y) is "x has visited y".
d) $\forall$x$\exists$yL(x,y), where L(x,y) is "x has learned programming language y", the domain for y is all the countries in the world.
e) $\exists$x$\exists$y$\forall$z(O(y,z)$\rightarrow$T(x,z)), where O(y,z) is "Department y offer course z", T(x,z) is "Student x has taken course z", the domain for y is all the departments in the school, the domain of z is all the courses in the school.
f) $\exists$x$\exists$y(G(x,t) $\land$ G(y,t)), where G(x,t) is "x grew up in town t", the domain for y is all the students in the class, the domain for t is all the towns in the world.
g) $\forall$x$\exists$y$\exists$z(C(x,y,z)), where C(x,y,z) is "Student x has chatted with student y in group z", the domain of y is all the students in the class, the domain of z is all the chat groups formed by the students.
