After attending this class the students able to Define proposition and logical connectives Give proof by truth tables Test the validity of argument using rule of logic Design simple circuits using basic gates and derive the logical expression for the given circuit

1. Discrete Mathematics(DM)
Dr.A.Senthilselvi B.E., M.Tech., Ph.D.,

2. Discrete Mathematics
Pre-request
After attending this class the students able to
• Define proposition and logical connectives
• Give proof by truth tables
• Test the validity of argument using rule of logic
• Design simple circuits using basic gates and derive the
logical expression for the given circuit

3. What is Discrete Mathematics?
Discrete Mathematics is the study of discrete objects
Discrete means: “ distinct or not connected”
Discrete Vs Continuous
Discrete objects: Ex- Natural Numbers, Digital Clock
Continuous object: Ex- Real Numbers, Analog clock

4. Why Discrete Mathematics?
It develops your mathematical thinking
Improve your problem solving ability
It is a foundational subject for different computer science subjects such
as compiler design, data bases, computer security, automata theory etc.
Many problems can be solved using DM

5. Topics included in the study of discrete math
Mathematical Logic
Combinatorics
Graph Theory
Group Theory
Set Theory

6. Propositional Logic

7. Why
Propositional
Logic?
Determine the output for the combinatorial
circuit in Figure 2.
How can this English sentence be translated
into a logical expression?
“You can access the Internet from campus
only if you are a computer science major or
you are not a freshman.”

8. Logical
Operators
● Conjunction
● Disjunction
● Negation
● Implication
● Bi-conditional

9. Conjunction
Let p and q be two Propositions.
Conjunction of a p and q is
denoted by p^q ,When both p
and q are true then the
Compound Proposition p^q is
true.
p q p ^ q
T T T
T F F
F T F
F F F

10. Disconjunction
Let p and q be two Propositions.
Conjunction of a p and q is denoted
by p ν q ,When both p and q are
FALSE then the Compound
Proposition p ν q is FALSE.
p q pν q
T T T
T F T
F T T
F F F

11. Let P be a Proposition.  P is
called negation of p which
simply states that “It is not the
case that p”
If P is TRUE then  P is FALSE.
If P is FALSE then  P is TRUE
Negation
P  P
T F
F T

12. Implication
Let p and q be propositions.
The proposition “if p then q”
denoted by pq is called
implication
p q pq
T T T
T F F
F T T
F F T

13. Biconditional
Let p and q be two
propositions. The
biconditional statement of the
form pq is the proposition
“p if and only if q.
p  q is true whenever the
truth values of p and q are
same.
p q p q
T T T
T F F
F T F
F F T

14. Reference
Discrete Mathematics and Its Applications, 7th Edition by
Kenneth Rosen

15. Thank you