Dsicrete Mathematics - Mid solutions - 29th June

gistfile1.txt

Question - 1   Ǝ ∀ ˄˅
a) A(Lois,Prof Michael)

b) ∀x S(x)-->A(x,Prof Gross)

c) 

d) Some student has not asked any faculty member a question
 Ǝx (S(x)˄∀y(F(y)-->~A(x,y) ) )

e) There is a faculty member who has never been asked a question by a student.
 Ǝx (F(x)˄ ∀y(S(y)-->~A(y,x) ) )]

f)
 Ǝx (S(x)˄ ∀y(F(y)-->~A(x,y) ) )]

g) 
 Ǝx (F(x)˄ ∀y (F(y)˄ x!=y --> A(x,y) ) )

h)
 Ǝx (S(x)˄ ∀y (F(y)--> ˄ A(y,x) ) )

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Question 2

a) True  
b) True
c) True
d) True
e) True
f) False
g) True
h) False

Ǝ ∀ ˄ ˅ 
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Question 3
a) True
b) False
c) False 
d) True

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Question 4
Direct, Indirect, Contradiction methods.

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Question 5
Show that if n is an integer


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Question 6





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Question 7
Induction for Harmonic Equation









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