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B7401

b) Define Pigeonhole principle. Show that in a group of 6 people, where any two

(4) people are either friends or Strangers, there are either 3 mutual friends or 3
mutual strangers

Module 1५
Solve + = 3r(2) (6)
OR
Solve -4 +3 = -200, 1110 ; given that 23000 , 53300 (6)
Module V

Let G= (४, E) be an undirected graph or multi graph with no isolated vertices. (6)
Show that G has an Euler circuit if and only if G is connected and every vertex in G has
even degree

OR
Use Fleury’s algorithm to find an Euler circuit for the following graph (6)

Module VI

a) Translate the sentence into a logical expression: "ठप cannot access the internet
(2) from campus only if you are a computer science major or you are not a
freshman”

b) Show that the following argument is valid: If today is Monday, I have a test in (4)

Physics or Mathematics. If my Physics professor is sick, I will not have a test in

Physics. Today is Monday and my Physics professor is sick. Therefore I have a
test in Mathematics”

OR
a) Negate the statement in logical form “There is an honest student”. (2) b) Use
rules of inference to show that $xM(x) follows logically from the premises (4)
(x) (061100) and $xH(x)

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