logical proof - discrete maths Watch

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yagmai
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Report Thread starter 13 years ago
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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.

this is my solution. i have not done the proving yet

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

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


2) all sce students know programming. all SCE students having business minor know accounting. alvin is an SCE student but he does not know accounting. francis knows accounting but he does not know programming. therefore, alvin does not haf business minor and francis is not an SCE student

this is my solution
Predicates:
SCE(x) : x is student of SCE
BM(x) : x taking business minor
A(x): x taking accounting
P(x): x know programming

∀x(SCE(x)->P(x))
∀x(BM(x)->A(x))
SCE(Alvin) ^ ~A(Alvin)
A(Francis) ^ ~P(Francis)
therefore, ~BM(Alvin) ^ ~SCE(Francsi)

SCE(Francis) -> P(Francis) ----- (1)
SCE(Alvin) -> P(Alvin) -----(2)
BM(Francis) -> A(Francis) --- (3)
BM(Alvin) -> A(Alvin) ---(4)

~A(Alvin) conjuntive simplification on 5
~BM(Alvin) modus tollen on 4
~P(Francis) - conjunctive simplification on 6
~SCE(Francis) - Modus tollen on 1

hence
~BM(Alvin) ^ ~SCE(Francis) - rules of conjunction

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

I'm stuck at proving it

d) 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))

e) All problems are difficult and frustrating. some problems are challenging. therefore some problems are challenging and frustrating.

D(x): x is difficult
F(x): x is frustrating
P(x): x is problem
C(x): x is challenging

how shld i approach this qns?
∀x(P(x) -> D(x) ^ F(x))
∃x(P(x) ^ C(x))
thus ∃x(C(x) ^ F(x))
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yagmai
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#2
Report Thread starter 13 years ago
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up. any1 who is gd in discrete math pls help. thanks alot
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