Discreet Mathematics Code-3748 4-th year (Hons.) Test Examination-2008

Govt. M. M. college, Jessore

Dept. of Mathematics

4-th year (Hons.) Test Examination-2008

Sub-Discreet Mathematics     Code-3748

Full Marks-50   Time-2.5 hours


[All questions are of equal value. Answer any four questions ]
  1. (a) Prove that is a irrational by contradiction.

(b) Use mathematical induction to prove that .

where , ,………..,are subsets of a universal set U and n is

a positive integer .


  1. (a) Define floor function, Ceilling function,Integer value function,

Absolute value function,logarithmic function and

exponential function

(b) Let x be any real number, then the following hold :

(i)  (ii) , m is any integer.


  1. (a) Prove that .

(b) How many integers between 1 and 300 are divisible by at least

one of 3, 5, 7? divisible by 3 and 5 but not by 7.


  1. (a) Let , n>1 be linear homogenous

recurrence relation with constant co-efficient . Let t be a non zero

real number , then the sequence  satisfies the above relation if

and only if .

(b) Solve the linear homogenous difference equation

  1. (a) Define Eulerian circuit. Let G be a connected plane graph with

V vertices, E edges and R regions, then prove V-E+R=2.

(b) Show that the following two graphs and are isomorphic

  1. (a) Define Capacity , Value of flow and Cut. Verify the law of

conservation of flow at a , e and d


(b) Define maximum flow. Find a maximum flow in the directed

network shown in the adjacent figure and prove that it is maximum,

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