Discrete Structure
-
Upload
syed-umair -
Category
Education
-
view
47 -
download
0
Transcript of 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.