Download DBATU B.Tech 2019 March 4th Semester Discrete Structures and Applications Question Paper

Download DBATU (Dr. Babasaheb Ambedkar Technological University) B Tech 2019 March (Bachelor of Technology) 4th Semester Discrete Structures and Applications Question Paper

DR. BABASAHEB AMBEDKAR TECHNOLOGICAL UNIVERSITY, LONERE
Mid Semester Examination ? March 2019
Course: B. Tech in Information Technology Sem: IV
Subject Name: Discrete Structures and Applications Subject Code: BTITC403
Max Marks: 20 Date: 13/03/2019 Duration:? 1 Hr.
Instructions to the Students:
1. Assume suitable data wherever necessary.
Select any one option from the following questions.
1. The cardinality of A = {5, 6, 3, 2, 3, 2} is
a) 6 b) 5 c) 4 d) 3
2. in a conditional statement, the ?rst part is the antecedent and the second part
is the...
a) Predicate b) Consequent c) Subject (1) Disjunct
3. A function is said to be if and only if f(a) = f(b) implies that a
= b for all a and b in the domain of f.
a) One?to?many b) One?to?one c) Many?to-many d) Many-to-one
4. Let f and g be the function from the set of integers to itself, de?ned by f(x) = 2x
+ 1 and g(x) = 3x + 4. Then the composition of f and g is
a)6x+9 b) 6x+7 c)6x+6 d)6x+8
5. A coin is tossed 3 times. Find out the number of possible outcomes.
a) None of these b) 8 c) 2 d) 1
6. Letters of SAP taken all at a time can be written in
a) 2 ways b) 6 ways c) 24 ways (1) 120 ways
Solve Any Two of the following.
Give reasons for each step needed to show that the following argument is valid.
[pA(99q)A(sVr)?(r->lq)l->(th)
Steps ' reasons
1) p
2) p9q
3) q
4) 1?") !q
5) q-)!r
6) !r
7) svr
8) s
9) svt
(Level/CO)
C01
C01
C02
C02
C02
C02
C01
Marks
6
3X2

(B)
(C)
Q. 3
(A)
(B)
Prove following for all n>=1 by the principle of mathematical induction.
12 + 32 +52 + .......... (2n?l)? = n (2n-1) (2n+l)/3
List all the combinations of size 3 that result for the letters m, r, a, f and t.
Solve Any One of the following.
In how many ways can 12 different books be distributed among 4 children so
that a) each child gets three books? b) the two oldest children get four books
each and the two youngest get two books each?
Let p(x), q(x) and r(x) be the following open statements.
p(x): x2-7x+10=0
q(x): xz-Zx-3=0
r(x): x<0
a) determine the truth or falsity of the following statements, where the universe
is all integers. If a statement is false, provide a counterexample or explanation.
1) VX [p(X) '9 ?(30] 2) 3X [q(X) 9F(X)]
b) find the answers to part a) when the universe consists of all positive integers.
*** End 9dr]:
C02
C02
C02
C01