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Mathematical Foundations of
Computer Science July 2023
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Code No: R2021054 R20 SET - 1
V IL A S R A O D E S H M U K H F O U N D A T IO N
D R B A B A S A HE B A M B E D K A R T EC HN OLOGY U N IV E R S IT Y, L ON E R E
R E G U L A R A N D S E M IS T E R E X A M IN A T ION -2 0 25
Course: B TECH Semister: IV
Branch : Electrical Engineering
Time: 3 hours Max. Marks: 70
DATE : 11/08/2025 Subject Name: MATHMATICS. III
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UNIT.I
1 a) Obtain POS of the following formulas [7M]
(i)(P ΛQ ΛR) V (~P ΛRΛQ) V(~P Λ~Q Λ~R)
b) Express the following statements using quantifiers. Then construct the negation [7M]
of the statement i) Every bird can fly ii) Some birds can talk
Or
2 a) Define well formed formula? Write in brief about well defined formulas. [7M]
b) Obtain POS of the following formulas: [7M]
(i)(P ΛQ ΛR) V (~P ΛRΛQ) V(~P Λ~Q Λ~R) (ii) PV(~P→(QV(~Q→R)))
UNIT-II
3 a) For any two sets A and B Prove the following Identity A-(A∩B) = A-B [7M]
b) Let A=(6,12,18,24,36,72), a ≤ b if and only if a divides b. Draw Hasse diagram [7M]
for it and prove that it is a lattice, but not a distributive lattice.
Or
4 a) If A={1,2,3,4} and P={{1,2},{3},{4}} is a partition of A. Find the equivalence [7M]
relation determined by P.
b) Draw the Hasse diagram for X={2,3,6,24,36,48} and relation ≤ be such that x≤y, [7M]
if x divides y
UNIT-III
5 a) A group of 8 scientists is composed of 5-psychologists and 3-sociologists, in [7M]
how many ways can a committee of 5 be formed that has 3- psychologists and 2-
sociologists.
b) How many ways can we distribute 14 indistinguishable balls in 4 numbered [7M]
boxes so that each box is non empty?
Or
6 a) Find the number of arrangements of the letters of MISSISSIPPI . [7M]
b) Out of 12 employees a group of four trainees is to be sent for software testing [7M]
and QA training of one month. (i) In how many ways a group of the four
employees be selected? (ii) what if there are two employees who refuse to go
together for training
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Code No: R2021054 R20 SET - 1
UNIT-IV
7 a) Solve the recurrence relation an-7an-1+12an-2 =0 for n≥2 where a0=1, a1=2. [7M]
b) Solve the recurrence relation using generating function an-6an-1=0 for n≥1 [7M]
wherea0=1.
Or
8 a) Find the general expression for a solution to the recurrence relation [7M]
an-5an-1+6an-2 =n(n-1) for n≥2
b) What is an nth order linear homogenous recurrence relation with constant [7M]
coefficients? Give examples.
UNIT-V
9 a) Draw binary search tree for the list : 2,1,5,6,8,9,7,3,4. [7M]
b) Find the chromatic number of the following i) Cn ii) Kn iii) Km,n [7M]
Or
10 a) Discuss in brief about BFS and DFS of a graph. [7M]
b) State and prove Euler’s formula for a plane connected graph. [7M]
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