Lab 4-Logic and Proof (1.4 -1.5)
Spring
2017
ePurposStatement
.solving exercises from the text book
Activity Outcome
By the end of this lab students will understand logic and proof and will be able to solve shorter/easier or longer /
harder problems given

Counting
College of Computing & Information Technology
King Abdulaziz University
CPCS-222 Discrete Structures
Basics of Counting
Section 5.1
Dr. Jonathan (Yahya) Cazalas
Counting
page 2
The Product Rule
If there are n1 ways to do task 1, and n2 ways to

King ABDUL AZIZ University
Faculty Of Computing and
Information Technology
CPCS 222
Discrete Structures I
Relations
Dr. Eng. Farag Elnagahy
[email protected]
Office Phone: 67967
Relations
Functions as Relations
Let A and B be nonempty sets.
A fun

King ABDUL AZIZ University
Faculty Of Computing and
Information Technology
CPCS 222
Discrete Structures I
Counting
Dr. Eng. Farag Elnagahy
[email protected]
Office Phone: 67967
The Basics of counting
Combinatorics is the mathematics of counting an

King ABDUL AZIZ University
Faculty Of Computing and
Information Technology
CPCS 222
Discrete Structures I
The Foundations: Logic and Proofs
Dr. Eng. Farag Elnagahy
[email protected]
Office Phone: 67967
1
Propositional Logic
Propositional logic is

Lab 1-Logic and Proof (Chapter 1.1)
Spring
2017
ePurposStatement
.solving exercises from the text book
Activity Outcome
By the end of this lab students will understand basic logic concepts, , and will be able to solve
shorter/easier or longer / harder pro

Lab 5-Logic and Proof(1.5 & 1.6)
Term 2
2017
ePurposStatement
.solving exercises from the text book
Activity Outcome
By the end of this lab students will understand predicates and quantifiers , logic programming , nested
quantifiers and will be able to so

Term2
Lab 6-Logic and Proof (chapter 1.6-1.8)
2017
ePurposStatement
.solving exercises from the text book
ActivityOutcome
By the end of this lab students will understand proof and will be able to solve shorter/easier or longer /
harder problems given in t

PREDICATES AND
QUANTIFIERS
Section 1.4
Summary
Predicate Logic (First-Order Logic (FOL),
Predicate Calculus)
The Language of Quantifiers
Logical Equivalences
Nested Quantifiers
Translation from Predicate Logic to English
Translation from English to

INTRODUCTION
TO PROOFS
Section 1.7
Section Summary
Mathematical Proofs
Forms of Theorems
Direct Proofs
Indirect Proofs
Proof of the Contrapositive
Proof by Contradiction
2
Motivation
A proof is a valid argument that establishes the truth
of a statement

Whats wrong with this proof ?
If you figure it out, do NOT say the answer
let others think about it as well.
1.
2.
3.
4.
5.
6.
7.
8.
Let a and b be non-zero such that
Multiply both sides by a
Subtract b2
Factor both sides
Divide by (a-b)
Since a = b, we

Mathematical
Induction
College of Computing & Information Technology
King Abdulaziz University
CPCS-222 Discrete Structures
Outline
Summations
Basically reviewing basics of summations
And how they tie into some induction problems
Mathematical Inductio

King ABDUL AZIZ University
Faculty Of Computing and
Information Technology
CPCS 222
Discrete Structures I
Set Theory
Dr. Eng. Farag Elnagahy
[email protected]
Office Phone: 67967
Set Theory
Set is the fundamental discrete structure
on which all o

Lab 2-Logic and Proof (Chapter 1.2 & 1.3)
Spring
2017
ePurposStatement
.solving exercises from the text book
Activity Outcome
By the end of this lab students will understand basic logic concepts, , and will be able to solve
shorter/easier or longer / hard

Lab 3-Logic and Proof (Chapter 1.2,1.3)
ePurposStatement
.solving exercises from the text book
Activity Outcome
By the end of this lab students will understand basic logic concepts, , and will be able to solve
shorter/easier or longer / harder problems gi

Lab 6-Logic and Proof (chapter 1.6-1.8)
Term2
2017
ePurposStatement
.solving exercises from the text book
ActivityOutcome
By the end of this lab students will understand proof and will be able to solve shorter/easier or longer /
harder problems given in t

CPCS-222, Data Structures
Summation Practice Problems
Evaluate the following sums (use the RULES from the PPT slides):
100
1)
(3i + 4)
i =10
2n
2)
i
i =5
4n
3)
n i
3
i =1
n
4)
i
4
i =1 j =1
100
i
i =10
5)
j =1
(1 + 12 j )
2n
6)
i
i = n 1
(2i + 3n )
2n

CPCS-222, Data Structures
Summation Practice Problems (Solutions)
Evaluate the following sums (use the RULES from the PPT slides):
100
100
100
i =10
1)
i =10
i =10
(3i + 4) = 3 i + 4 = 3
2n
2)
i =
i =5
(5 + 2n)(2n 4)
= (2n + 5)(n 2)
2
4n
3)
4n
n i = n i

King ABDUL AZIZ University
Faculty Of Computing and
Information Technology
CPCS 222
Discrete Structures I
Functions
Dr. Eng. Farag Elnagahy
[email protected]
Office Phone: 67967
Functions
Let A and B be nonempty sets.
A function f from A to B is

Fun With Summations
College of Computing & Information Technology
King Abdulaziz University
CPCS-222 Discrete Structures
Summations
Definition:
In very basic terms, a summation is the addition of a
set of numbers.
Example:
Lets say we want to sum the in

Strong Induction
College of Computing & Information Technology
King Abdulaziz University
CPCS-222 Discrete Structures
Mathematical Induction
Just a review
Dr. Jonathan (Yahya) Cazalas
Strong Induction
page 2
Mathematical Induction
Example: Infinite Ladd

King ABDUL AZIZ University
Faculty Of Computing and
Information Technology
CPCS 222
Discrete Structures I
Sequences and Summations
Dr. Eng. Farag Elnagahy
[email protected]
Office Phone: 67967
Introduction
Sequences are ordered lists of elements.

Faculty of Computing and
Information Technology
CPCS 222
Discrete Structures I
Spring 2017
Faculty of Computing and
Information Technology
Dr. Zeinab Eid
[email protected]
Office#: S- 105,
Office Hours: Monday & Wednesday 11:00 -12:30
Dr. Amal AlManso