Counting

Mutiplication principle in Counting

By : Hariz and Fizul

Additional Principle in Counting

By : Leemuni

Combining principle of Counting

By : Zarif and Aien

Permutation

By : Siti and Ridha

Combination

By : Dila

Pigeonholes

By : Izah

Euler And Hamilton

Definition of Euler Path and Circuit

By : Siti and Ridha

Properties of Euler

By : Izah 

Euler And Hamilton [full version]

Mathematical Induction I & II

Basis Step

By : Hariz

Inductive Step

By : Fizul & Zarif

Inductive Hypothesis

By : Muni & Leem

Step for ease finding formula

By : Norizah

Divisibility I

By : Siti

Divisibility II

By : Dilla 

Inequalities
By : Aien

Chapter 4

Definition of sequence

By : Fizul

Example Problem involving Sequence.

By : Norizah

Types of Sequence

By : Siti

Example Sequence use in Computer Programming

By : Zarif & Hariz

The Principle of Mathematical Induction

By : Leem & Muni

The Method of Proof by Mathematical Induction

By : Ridha

2 Example Problems that Use for solving Mathematical Induction

By : Dilah & Aien

Chapter 3

Sets using computer.

By : Norizah & Aien

Relation Between 2 Sets

By : Siti

Properties of relation

By : Hariz

Definition or concept of Function on General Sets.

By : Zarif

Boolean Function

By : Dilla

Types of Function

By : Leem

Inverse Function

By : Muni

Composite Function

By : Fizul

chapter 2

Way of listing the element of sets & Specifying properties of sets.

 By : Aien

Set membership

By : Ridha

Set of numbers & Set Equality

By : Muni

Subset

By : Siti

Power Set

Set operation (Union and Intersection set)

By : Leem

Set operation ( Disjoint set )

By : Hariz

Set operation ( Set complimentary )

By : Fizul

Generalized unions intersection

By : Zarif

Cartesian Product

By : Leem

chapter 2 [full version]

First exersice

Exercise:

p = Swimming at the Pork Dickson shore is allowed.

q = Sharks have been spotted near the shore.

Express each of the compound propositions as an English sentence.

a)   ¬p

b)  p ^ q

c)   ¬p ˅ q

d)  p → ¬q

e)   ¬q → p

f)   ¬p → ¬q

g)   p ↔ ¬q

h)  ¬p ^ (p ˅ ¬q)

Need answers ? Let's check this out :)

exercise answer

chapter 1

Proposition

by : Dila and Ridha

Type of Truth Table

by : Aien

Propositional Equivalances

by : Leem, Muni and Siti

Predicates and Quantifiers

by : Fizul, Hariz, Zarif

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