Download SGBAU BCA 2019 Summer 1st Sem Discrete Mathematics Question Paper

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B.C.A. (Part-I) Semester-I Examination

DISCRETE MATHEMATICS

Paper-1ST5S

Time : Three Hours] [Maximum Marks : 60

Note :— Attempt one question from each unit.

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UNIT-I

1. (a) Among the integers 1 to 1000, how many are not divisible by 5 and 7 but divisible by 3? 6
2. (b) State and prove principle of inclusion exclusion for three sets. 6

1. (p) Define : (i) one-one function (ii) onto function (iii) composite function. Give one example of each. 6
2. (q) Define Countability and prove that if A and B are Countable then A*B is also countable. 6

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UNIT-II

1. (a) Define ordinary generating function and exponential generating function. Determine the sequence for the generating function : (1) e (2) (1! 6
2. (b) Define Ferrer's and Conjugate Ferrer's diagram and Draw both 7+5+3+2+1 of 18. 6

1. (p) Find the coefficient of x'® in the series (x*+x*+x*+.....)% 6
2. (q) Define probability generating function and prove that E(x) = P'x(1). 6

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UNIT-III

1. (a) Define Recussive formula and find recurrence relation for the infinite sequence : 1) 3:7,11515;19,23..... (i) 4,6,8,10,12,..... 6
2. (b) Find particular solution of a — 7a_ + 10a_, = 8r+ 6 6

1. (p) Find Homogeneous solution of a — 8a_, + 16a_, = 0 with initial conditions a, = 16, a, = 48. 6
2. (q) Find Total solution of a_— 10a_, + 25a , = 2 6

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UNIT-IV

1. (a) Find the truth values of the following statements : (1) 2+5=7 and 4+2=6 (i) 10+2=7 or 11+2=14 (iii) 1+3=9 and 2+5=7 (iv) 4+2=7 and 3+7-10 (v) 13+2=15 or 10+3=13 (vi) 1+1=2 and 2+4=6 6
2. (b) Prove that both join and meet operations are associative. 6

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l irBtoankes'soehnjce and mcet operations are distributive. . 6

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1. Find the duals of the followingz : (i) an(avb)=a (i) an(bac)=(anrb) (iv) (av b)1 (vi) a< 0 6

UNIT-V

1. (a) Prove that in a distributive lattice if an element has complement then this complement 1s unique. 6
2. (b) If B is the sets of statements from closed under A, v and ~. Show that B Ko .t > is Boolean algebra where C is contradiction and t is tautology. 6

1. (p) If a distributive lattice if zero and unit element is complemented then prove that for any X, the inverse x' is unique. 6

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2. (q) Find disjuction normal form of (xvy)Aa(x'vy"). 6