BCA-02
June 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. Write answer as per the given instructions.
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 is thirty words.
Express the following set in Roster method:
A x x is a odd month of the year
Define Identity Relation.
Define binary number system.
Write the negation of the following statement:
p:3 is a natural number.
Define fallacies.
Define inverse of a element in a set for operation*.
220
BCA-02 300 4 (P.T.O.)
220
BCA-02 300 4 (Contd.)
Define poset.
(viii)Prove that If R is a ring with unity, then unity is unique.
Define a subgroup.
Write De-Morgen's law for Boolean Algebra.
Section B 4 × 10 40
Short Answer Questions
Note: Section contain 08 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.
In a village of 1000 families it was found the 40% families
have agriculture profession. 20% families have milk product
profession and 10% families have other profession. If
families have both agriculture and milk product profession
have milk product and other profession and have agriculture
and other profession and families have all these profession
find the number of family which have
Only agriculture profession.
Only milk product profession.
No profession.
If R is Relation N × N defined R ab= bc6(a,
and N N then prove that R is equivalence relation.
Solve:
(2322)8
(233)10
(5C5)16
(101010010001)2
BCA-02 300 4 (P.T.O.)
220
Using truth table, prove that
p*q " "
Prove that dual of a lattice is again a lattice.
Prove that a group of order less than 5 is Abelian.
Prove that a non-zero finite integral domain is a field.
Simplify the three variable Boolean expression P
using Boolean algebra.
Section C 2 × 20 40
Long Answer 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) Prove that following propositions are tautology:
" 0
" " q
Prove that following propositions are fallacies:
0
0 p
11) Prove that a Boolean algebra with 3 distinct elements is not
possible.
Prove that union of two subgroups is a subgroup if and
only if one is contained in other.
220
BCA-02 300 4
12) Draw the logic circuit for Boolean expression
x).
Show that the logic circuits and shown in figure are
equivalent.

13) Explain following computer codes
ASC II
UNICODE
Prove that If B and C are any sets then