This is a Question Papers of Mumbai University for B.Sc.IT Student of Semester - III [Logic, Discrete Mathematical Structures] (Old Course). [Year - April / 2014] . . .Solution Set of this Paper is Coming soon...

1. M u m b a i B . S c . I T S t u d y
F a c e b o o k / m u m b a i b s c i t | I n s t a g r a m / k t . b s c i t
Page 1 | L o g i c D i s c r e t e M a t h e m a t i c a l S t r u c t u r e s
Q u e s t i o n P a p e r ( A p r – 2 0 1 4 ) [ O l d C o u r s e ] B Y K a m a l T .
– Kamal T.
Time: 3 Hours Total Marks: 100
N.B.: (1) Questions No. 1 is Compulsory.
(2) Attempt any four questions from question No. 2 to 6.
Q.1 Attempt Both The Question: (10 Marks)
(A) State and prove DeMorgan’s Laws for sets. (5)
(B) Consider the Boolean Polynomial 𝑝(𝑥, 𝑦, 𝑧) = (𝑥 ∧ 𝑦) ∨ (𝑥 ∨ (𝑦′
∧ 𝑧)). Construct
truth table for function 𝑓: 𝐵3 → 𝐵 determined by this polynomial. Draw the logic
diagram.
(5)
Q.2 Attempt Both The Question: (20 Marks)
(A) Write a note on: –
(i) Union of two sets (ii) Complement of a set.
Illustrate using Venn-Diagram.
(10)
(B) What are properties of Mathematical structures? (10)
Q.3 Attempt Both The Question: (20 Marks)
(A) Show that any two equivalence classes are equal or disjoint. (10)
(B) Find 𝑅∞
using Warshall’s Algorithm
𝐴 = {1, 2, 3, 4} and 𝑅 = {(1,1) (1,2) (2,3) (3,4)}
(10)
Q.4 Attempt Both The Question: (20 Marks)
(A) Check if 𝑓(𝑛) and 𝑓(𝑛) have same order.
(i) 𝑓(𝑛) = log(𝑛) and 𝑔(𝑛) = log(𝑛).
(ii) 𝑓(𝑛) = 5𝑛2
+ 4𝑛 + 3 and 𝑔(𝑛) = 𝑛2
+ 100𝑛.
(10)
(B) (i) Determine whether given pair of graph is isomorphic.
(ii) Show that (IR+
, *) is abelian group. IR+
is set of all nonzero real numbers and *
is defined as 𝑎 ∗ 𝑏 =
𝑎𝑏
2
.
(10)

2. M u m b a i B . S c . I T S t u d y
F a c e b o o k / m u m b a i b s c i t | I n s t a g r a m / k t . b s c i t
Page 2 | L o g i c D i s c r e t e M a t h e m a t i c a l S t r u c t u r e s
Q u e s t i o n P a p e r ( A p r – 2 0 1 4 ) [ O l d C o u r s e ] B Y K a m a l T .
– Kamal T.
Q.5 Attempt Both The Question: (20 Marks)
(A) Using Prim’s Algorithm find Minimal Spanning Tree beginning at Vertex E. (10)
(B) Let A=IN and R be relation on A such that xRY if 𝑥 ≤ 𝑦. Show that R is a partial order
and (𝐼𝑁, ≤ is a poset.
(10)
Q.6 Attempt Both The Question: (20 Marks)
(A) Write a note on Languages and concatenation. (10)
(B) Design FSM which recognizes that languages in which every sentence end with 100. (10)