Discrete Math

hi all,

I encountered some qns which i am clueless on how to solve it. however i did some of the qns which i hope u guys can help me to take a look if I did it correctly

a) if it rains, then u come to the sch if ur sis spares an umbrella for you. It rains, but ur sis has not spared the umbrella for u. thus, u do no come to the school.

Let
x = it rains
y = you come to school
z = your sister spares an umbrella for you

x -> z -> y
x
~z
Therefore, ~y

Proving

x->z->y
x
therefore: z->y (modus pollen)

what shall I do next?

(2)
Every1 shouts or cries. not every1 cries. hence , some pple shout and dun cry.
is this correct?
S(x): x shouts
C(x): x cries

∀x(S(x) -> C(x))
∃x(~C(x))

thus. ∃x(S(x) ^ ~C(x))


(3)

If we are not going terminal 1 then we must be going to the MRT station and not to the airport. If we find Hotel Blue Lagoon on the eay then we are going to the airport. If we find hotel regal then we are not going terminal 1. we are not going thru the correct route. we find hotel regal on the way or we are going on the correct route. this implies that, if we are going to hotel blue lagoon then we going on the correct route.

Let
p = we are going to terminal 1
q = we are going to the MRT station
r = we are going to the airport
s = we find Hotel Blue Lagoon
t = we find Hotel Regal
u = we are going through the correct route

~p -> q ^ ~r
s -> r
t -> ~p
~u
t v u
Therefore, s -> u

this cannot be proven correct??
I am greatly appreciate ur help
.