Discrete Structures BS Mathematics/MS Mathematics 2 Semester/Term PU — University of the Punjab 2024
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BS ZOOLOGY first semester Animal diversity ZOOL 101 - university of Punjab 2025
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Literary criticism
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this paper consists of 60 marks but now we have 35 marks paper.
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Can you please tell me more past papers please because my exams are starting from next week
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Did you provide the past papers of the science of society uos?
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Paper text
UNIVERSITY OF THE PUNJAB
B.S. 4 Years Program / Second Semester - Fall 2024
Paper: Discrete Structures
Coures Code: CC-111
Roll No.
-...
THE ANSWERS MUST BE ATTEMPTED ON THE ANSWER SHEET PROVIDED
Q.1. Answer the following short questions:
1. Is the "divides" relation on the set of positive integers symmetric? la it
(6x5=30)
antisymmetric?
2. How many positive integers not exceeding 100 are divisible either by 4 or by
67
3. Give a big-O estimate of the function /(n) = n log (n? +
1) + n°log n.
4. A groop of 40 students were asked abour their faverite subjocrs: 25 like meth,
20 like science, and 12 like both. How many students like neither math nor
science?
3. An office building contains 27 floors and has 37 offices on each floor. How
many offices are in the building?
- Give an example of two uncountable sets A and B such that A -B is
a. finite.
b, countably infinite.
c. uncountable.
Answer the following questions:
(3x10=30)
Questios 2., A bowl contains 10 red balis and 10 blue bolls. A womas sclects balls
at random without looking at them.
a) How many bails must she sclect so be sure of kaving at Icast thee bails of the
same color?
b) How many balls must she select to be sure of having at least three blue balls?
Question
3. Let P(x). Q(x), R(x), and S(s) be the statements "x is a duck,""x la one
of my poultry." "x is an officer," and "r is willing to waltz," respectively. Express
each of these statements using quantifiers; logical connectives; and P(x). Ora). R/x).
and S(x).
a) No ducks are willing to waltz.
b) No officers ever decline to waltz.
e) All my poultry are ducks.
d) My poultry are not officers.
Qucstion
4. Supposc that A is thc act of sophomores it your school ind B is the sct
of students in discrete mathematics at your school. Express each of these sets in
terms of A and B.
a) The set of sophomores taking discrete mathematics in your school
b) The set of sophomores at your school who are not taking discrete
mathematica
a) The set of students at your school who either are sopbomores or are taking
discrete mathematics
d) The set of students at your school who either are not sophomores or are not
taking discrete mathematics
