This document is a presentation summary for the subject "Discrete Mathematical and Logic (DML)" by Sunipa Bera. It begins by acknowledging help from God, teachers, parents, and friends. It then defines basic concepts in propositional logic like propositions, compound propositions, propositional variables, truth values, and atomic propositions. It provides examples of true and false propositions. It defines logical operators like conjunction, exclusive or, disjunction, and negation. It gives truth tables for these operators. Finally, it lists topics covered in the presentation like translating English sentences, Boolean searches, and logic puzzles.

1. Name:- Sunipa Bera
B. Tech CSF- S.Y
Roll no. 17
PRN No:- 1901105181016
Subject:- Discrete Mathematical and Logic (DML)

2. Acknowledgment
Primarily I would thank God for being able to complete this
presentation in Success. Then I would like to thank my
teacher, whose valuable guidance has been the ones that
helped me patch this presentation and make it full proof
success her suggestions and her instructions has served as
the major contribution towards the completion of the
presentation.
I would like to thank my parents and friends who have
helped me with their valuable suggestions and guidance.

3. Proposition & Logical Operations

4. Proposition
A Proposition is a declarative sentence ( that is, a sentence that declares a fact) that is either true or false, but not both.
Example:- 1. Washington D.C. is the capital of United States of America
2. Toronto is the capital of Canada.
3. 1+1= 2
4. 2+2= 3
Proposition 1 & 3 is true whereas. Proposition in 2 & 4 are False.

5. Compound Proposition
Propositional Logic
Prepositional Variable
Truth Value
Atomic Proposition
The area of logic that deals with
propositions is called the Propositional
Calculus or Propositional Logic.
A mathematical Statements are constructed by combining one
or more propositions. New propositions, called compound
propositions, are formed from existing propositions using
logical Operators.
We use letters to denote proposition variables ( or sentential
variables), that is, variables that represent propositions, just as
letters are used to denote numerical variables. The conventional
letters used for prepositional variables are p, q, r, s, …
The truth value of the proposition is true, denoted
by T, if it is a true proposition, and the truth value of a
proposition is false, denoted by F, if it is a false
proposition.
Proposition that cannot be expressed in
terms of simpler propositions are called
atomic proposition

6. Definition 1
Definition 2
Definition 3
Definition 4
Let p and q be propositions. The
conjunction of p and q, denoted
by p ^ q is true when both p and q
are true and is false otherwise,
Let p and q be propositions, The
exclusive or of p and q, denoted
by p ⊕ q (or p XOR q), is the
proposition that is true when
exactly one of p and q is true and
is false otherwise.
Let p and q be propositions. The
disjunction of p and q, denoted by
p ν q, is the proposition “p or q”.
The disjunction p ν q is false
when both p and q are false and is
true otherwise.
Let p be a proposition. The negation of p,
denoted by ┐p (also denoted by p), is the
statement.
“It is not the case that p”
The preposition ┐p is read “not p”. The
truth value of the negation of p, ┐p, is the
opposite of the truth value of p.

7. Definition 2
Definition 3
Definition 4
Definition 1
p ┐p
T F
F T
p q p ^ q
T T T
T F F
F T F
F F F
p q p ⌵ q
T T T
T F T
F T T
F F F
p q p ⊕ q
T T F
T F T
F T T
F F F

8. 01 02 03 04 05
Translating
English
Sentence
System
Specifications
Boolean
Searches
Logic Puzzles Logic Circuit

9. Bibliography

10. T H A N K S .