Discrete Structure

Assigned To:

Syed Muhammad Umair Shah

Azra Ramzan

BS(CS) 2nd Semester

Indus International Institute D.G.Khan

Definition of Discrete Mathematics Difference between Discrete Mathematics &

continues

LOGIC

SIMPLE STATEMENT COMPOUND STATEMENT

LOGICAL CONNECTIVES & SYMBOLICREPRESENTATION

TRANSLATING FR0M ENGLISH TO SYMBOLS

TRANSLATING FROM SYMBOLS TO ENGLISH

WHAT IS TRUTH TABLE

Negation, Conjunction & Disjunction

Discrete Mathematics concerns processes that

consist of a sequence of individual steps.

Discrete mathematics is the study of

mathematical structures that are fundamentally

discrete rather than continuous.

:

sequence of individual steps is called D.M

Continuing without stopping; Sequence of

continuing step is called Continues

Logic is the study of the principles and

methods that difference between a valid

and an invalid argument.

Is the study of reasoning

Specifically concerned with whether

reasoning is correct.

Focuses on the relation among statement

as opposed to the content of any

particular statement.

A statement is a declarative sentence

that is either true or false but not both.

1. Grass is green.

2. 4 + 2 = 6

3. 4 + 2 = 7

4. There are four fingers in a hand.

Simple statements could be used to build a

compound statement

1. 3 + 2 = 5 Lahore is a city in

Pakistan

2. The grass is green It is hot today

3. Discrete Mathematics is difficult

to me

4. Ali is very rich

AND, OR, NOT are called LOGICAL

CONNECTIVES

Statements are symbolically represented by

letters such as p, q, r,...

:

p = “Islamabad is the capital of Pakistan”

q = “17 is divisible by 3”

NEGATION NOT

˜TILDE

CONJUNCTION AND ^ HAT

DISJUNCTION OR v VEL

CONDITIONAL IF……THEN

ARROW

BICONDITIONAL IF AND ONLY IF

DOUBLE ARROW

p ∧ q = Islamabad is the capital of Pakistan

17 is divisible by 3

p ∨ q = Islamabad is the capital of Pakistan

17 is divisible by 3

~p = Islamabad is the capital of

Pakistan

~p = Ali is a my best friend

Let p = “It is hot”, and q = “It is sunny”

1. It is hot. ~ p

2. It is hot sunny. p ∧q

3. It is hot sunny. p ∨ q

4. It is hot sunny. ~ p ∧q

Let m = “Ali is good in D.M”

c = “Ali is a Computer Science student”

1. ~ c = Ali is a Computer Science

student

2. c ∨ m = Ali is a Computer Science student

good in D.M.

3. m ∧ ~c = Ali is good in D.M not a

Computer Science student

A truth table specifies the truth value of a

compound proposition for all possible truth

values of its constituent proposition.