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

Download SGBAU (Sant Gadge Baba Amravati university) BCA 2019 Summer (Bachelor of Computer Applications) 1st Sem Discrete Mathematics Previous Question Paper

AVV?l 790
B.C.A. (Part?l) Semestcr?l Examination
DISCRETE MATHEMATICS
Paper?l STS
'l?imc : Three Hours] [Maximum Marks : 60
Note :? Attempt one question from each unit.
UNIT?I
l (21) Among the integers 1 to 1000, how many are not divisible by 5 and 7 but divisible by
3 ? 6
(b) State and prove principle of inclusion exclusion for three sets. 6
2. (p)
(q)
3 (a)
(b)
4. (p)
(q)
5. (a)
(b)
6 (P)
(q)
7 (a)
0?)
De?ne : (i) one-one function (ii) onto function (iii) composite function. Give one
example of each. 6
De?ne Countability and prove that ifA and B are Countable then Ax B is also countable
()
UNIT?Il
De?ne ordinary generating function and exponential generating function. Determine
the sequence for the generating function :
(1) e" (2) (1 'X)? 6
De?ne Ferrer?s and Conjugate Ferrer?s diagram and Draw both 7+5+3+2+ 1 of 18. 6
Find the coef?cient of x? in the series (x3+x3+x?+.....)5. 6
De?ne probability generating function and prove that E(x) : P'x(1). 6
UNIT?III
De?ne Recussive formula and ?nd recurrence relation for the in?nite sequence :
(i) 3.7.11,15,19,23 ..... (ii) 4,68,10,12, ..... 6
Find particular solution of ar ? 72177 + 10a?2 = 8r + 6 6
1
Find Homogeneous solution of ar ? 8ar_l + 16ar 1 '? 0 with initial conditions a2 = 16.
a. = 48. 6
+ 25a, 2 r: 2 o
L'NIT?IV
Find Total solution of ar ?? 10ar_I
Find the truth values of the following statements :
(i) 2+5=7 and 4+2??6 (ii) 10+2=7 0r 11"2'?14
(iii) l+3*?9 and 2+5=7 (iv) 4+2=7 and 3+7?10
(v) 13+2715 or 10+3=13 (vi) 1+1=2 and 2+4=6 6
Prove that both join and meet operations are associative. 6
YBC 15354 1 (com)

8. (p) Prm'c that boxh jwii? 311d :m-gt operations are digiribunw. b
(q) Find the duals of the iollm'ving :
9 (a)
(b)
10? (p)
(Li!
YBCVIS
L.)
(i) a 2 b
(ii) a A (a v b) r 3
(iii) a A 4b x c) : {a A hi
(iv) (a v b) S b
(v) 5' 2 1
(vi) a s U 6
UNIT?\?
Prove that in a disti'ibutiw lattice if an clement has complement then this complement
is unique. 6
If B is the sets, 01' statements from closed under A, v and Show that
-< B, A , v. ~, c. t > is Boolean algebra where C is cnmradiction and t is tautology.
6
If a distributive lattice if 7cm and unit element is complemented then pro '3 that for
any x, the inverse x' is unique. 6
Find disjuction normal form 01? (xvy)/\(x'vy'). 6
I
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