BCA-02
December Examination 2017
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 Type 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 is thirty words.
Express the following set in Roster method:
A
x x is a prime number 10}.
Define Cartesian product of sets.
Define binary number system.
Write the negation of the following statement:
p:5 is a prime number.
220
BCA-02 200 4 (P.T.O.)
220
BCA-02 200 4 (Contd.)
Define Tautology.
Define identity element.
Define Cyclic group.
(viii) Define Boolean Algebra.
Define integral domain.
Write absorption law for Boolean Algebra.
Section B 4 × 10 40
(Short Answer Type Questions)
Note: Section contain 08 short Answer Type Questions. Examinees
will have to answer any four question. Each question is of
10 marks. Examinees have to delimit each answer in maximum
200 words.
A survey shows that 63% of Indians like cheese where 76%
like apples. If of Indian like both cheese and apples find the
value of x.
Prove that Relation R defined on any non-void set A as
∈ R ⇔ a b is partial order Relation.
Solve:
(156)8
(296)10
(5C5)16
(10111010001)2
BCA-02 200 4 (P.T.O.)
220
Using truth table, prove that
p ↔ q ≡ → →
If d are elements of lattice such that a b and c d
then prove that a c b d
Prove that set G ω2} is cyclic group for multiplication of
complex numbers where ω2 are cube roots of unity.
Prove that any finite non-empty subset H of a group G is subgroup of
G if and only if a ∈ b ∈ H ⇒ ab ∈ H.
Simplify the three variable Boolean expression using
Boolean algebra.
Section C 2 × 20 40
(Long Answer Type Questions)
Note: Section contain 04 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.
10) If B and C are any sets then prove that
A
A
11) Prove that
p ≡
p ≡
220
BCA-02 200 4
12) Prove that finite commutative ring without zero divisors is a
field.
State and prove Lagrange's theorem for subgroups.
13) Show that the logic circuits and shown in figure are
equivalent.

Explain following computer codes.
ASC II
UNICODE