BCA-02
December Examination 2016
BCA Pt. I Examination
Discrete Mathematics
Paper BCA-02
Time 3 Hours Max. Marks 100
Note: The question paper is divided into three sections B and C.
Section A 10 × 2 20
(Very Short Answer Questions)
Note: Section contain 10 Very Short Answer Type Questions. Examinees have to attempt all questions. Each question is of 02 marks and maximum word limit may be thirty words.
Specify the set
A
is even positive number and 1 x in Roster form
Define a Tautology.
Define Domain and range of a relation.
Define maximal and minimal elements in a poset.
Define a bijective function.
Define a Binary operation.
State Lagrange's theorem for groups.
(viii) Explain duality in Boolean algebra
220
BCA-02 200 4 (P.T.O.)
BCA-02 200 4 (Contd.)
220
Explain conjunctive normal form (CNF).
Write names of universal gates.
Section B 4 × 10 40
(Short Answer Questions)
Note: Section contain eight short answer type questions. Examinees
will have to answer any four questions. Each question is of
10 marks. Examinees have to delimit each answer in maximum
200 words.
Solve:
(C2BA)16
(7437)8
(11000101)2
(100111.101)2
Using laws of algebra of sets prove that
A B A B1
A B B
Verify whether p s is valid conclusion of the premises
p " s q
Prove that relation R defined on set of positive integers such that
a b is even} is an equivalence relation.
In a group G prove that
a for all a e G
b-1a-1 for all b e G
BCA-02 200 4 (P.T.O.)
220
If m is a fixed positive integer then prove that the set
s m z x x e is a subring of ring (z1 1x)
In a Boolean algebra show that a b. If and only if a1b ab1 0
Transform the following Boolean expression into disjunctive
normal form x1 x1x2 x1x2x3
Section C 2 × 20 40
(Long Answer Questions)
Note: Section contain 4 Long Answer Type Questions. Examinees
will have to answer any two questions. Each question is of
20 marks. Examinees have to delimit each answer in maximum
500 words. Use of non-programmable scientific calculator is
allowed in this paper.
10) Explain the following logic gates
NOR GATE
NANO GATE
XOR GATE
XNOR GATE
11) Explain following computer codes
UNI CODE
EBC DIC
BCD
ASCII
BCA-02 200 4
220
12) If c and d are arbitrary elements of a lattice then prove
that
a b and c d a c b d
a 0 a
a 0 0 0 vc
a b a 0 b b
13) Prove that a non-empty subset H of a group G is a sub group
of G If and only If ab-1 is in H whenever a and b are in H.
Show that elements in a group G which commute with every
element of G forms a sub group of G.