number of the form NXX-NXX-XXXX. How many different
telephone numbers would be available worldwide under this numbering
plan?
How many positive integers between 100 and 999 inclusive
i) are divisible by 7?
ii) are not divisible by 4?
iii) are divisible by 3 and 4?
iv) are divisible by 3 or 4?
v) are divisible by 3 but not by 4 and 7?
For the relations R
1
={(a,b), (a,c), (b,d), (d,d)} and R
2
={(a,a), (a,d),
(b,a), (b,b), (c,e), (d,d), } on sets {a,b,c,d,e} to {a,b,c,d,e} determine
R
2
◦R
1.
Represent the output relation using directed graph.
Consider the following relation R={(1,1),(1,2),(1,3),(1,4),
(2,2),(2,3),(2,4),(3,3),(3,4),(4,4)} defined over the set S={1,2,3,4}
i) Is (S,R) is a Poset? Justify your answer.
ii) Is (S,R) Linearly ordered? Justify your answer.
iii) Is (S,R) Well-ordered? Justify your answer.
iv) Identify the minimal, maximal, greatest and least elements
v) Identify the lower bound and upper bound for the set {3}and
also find the least upper bound and greatest lower bound.
In how many possible orders a student can answer 5 questions in the
SEE exams considering the following conditions
i) There are 3 units UNIT1, UNIT2 and UNIT3 consisting of 3, 3
and 2 questions respectively.
ii) Student has to answer 2 questions from UNIT 1 , 2 questions
from UNIT 2 and one from UINIT 3
In order to conduct the SEE examination, In how many ways seating
arrangement can be made for 240 CS students and 240 EC students
such that CS and EC students should sit alternatively.
School of Computer Science and Engineering is planning to create a
Computer network lab of 15 computers. In how many ways every
computer is connected to every other computer for each of the
following assumptions.
i) Every computer is implicitly connected to itself
ii) Every computer is explicitly connected to itself
iii) Every connection is one-way communication
iv) Every connection is two-way communication
All India Council for Technical Education
Computer Science and Engineering