The document defines discrete mathematics and contrasts it with continuous mathematics. It discusses logic, statements, logical connectives, translating statements to symbolic representations, and truth tables. Discrete mathematics concerns processes with discrete, individual steps rather than continuous sequences. Logic studies valid vs invalid reasoning and the relationships between statements. Simple statements can be combined using logical connectives like negation, conjunction, and disjunction to form compound statements. Truth tables specify the truth value of compound propositions based on the truth values of their constituent propositions.

1. Assigned To:
Syed Muhammad Umair Shah
Azra Ramzan
BS(CS) 2nd Semester
Indus International Institute D.G.Khan

3.  Definition of Discrete Mathematics
 Difference between Discrete Mathematics &
continues
 LOGIC
 SIMPLE STATEMENT
 COMPOUND STATEMENT
 LOGICAL CONNECTIVES & SYMBOLIC
REPRESENTATION
 TRANSLATING FR0M ENGLISH TO SYMBOLS
 TRANSLATING FROM SYMBOLS TO ENGLISH
 WHAT IS TRUTH TABLE
 Negation, Conjunction & Disjunction

4.  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.
:

5.  sequence of individual steps is called D.M
 Continuing without stopping; Sequence of
continuing step is called Continues

6.  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.

7.  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.

8.  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

9.  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”

10. NEGATION NOT
˜
TILDE
CONJUNCTION AND
^ HAT
DISJUNCTION OR
v VEL
CONDITIONAL IF……THEN
 ARROW
BICONDITIONAL IF AND ONLY IF
 DOUBLE
ARROW

11.  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

12.  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

13.  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

14.  A truth table specifies the truth value of a
compound proposition for all possible truth
values of its constituent proposition.