Discrete Mathematics Notes, Lecture notes of Discrete Mathematics

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MTH-401: DISCRETE MATHEMATICS

Department of Mathematics

Lovely Professional University 28.07.

List of topics for today’s class

• Proposition
• Propositional logic
• Logical connectives
• Truth tables

Importance of Mathematical Logic

The rules of logic give precise meaning to mathematical statements. These rules are used to distinguish between valid and invalid mathematical arguments. Apart from its importance in understanding mathematical reasoning, logic has numerous applications in Computer Science, varying from design of digital circuits, to the construction of computer programs and verification of correctness of programs.

Proposition

STATEMENT - A sentence which is either TRUE or FALSE. Examples :

Proposition

STATEMENT - A sentence which is either TRUE or FALSE. Examples : (a) Let her go. No.

Proposition

STATEMENT - A sentence which is either TRUE or FALSE. Examples : (a) Let her go. No.

(b) 5 is greater than 7.

Proposition

STATEMENT - A sentence which is either TRUE or FALSE. Examples : (a) Let her go. No.

(b) 5 is greater than 7. Yes

(c) Dog is an animal.

Proposition

STATEMENT - A sentence which is either TRUE or FALSE. Examples : (a) Let her go. No.

(b) 5 is greater than 7. Yes

(c) Dog is an animal. Yes

Proposition

A proposition is a collection of declarative statements that has either a truth value ”true” or a truth value ”false”. It cannot have both the both the truth values ”TRUE” and ”FALSE”. The truth value ”TRUE” and ”FALSE” are denoted BY ”T” and ”F” respectively.

Propositional logic

Propositional logic studies the ways statements can interact with each other.

Propositional logic

Propositional logic studies the ways statements can interact with each other. Propositional logic does not really care about the content of the statements. For example, in terms of propositional logic, the claims, “if the moon is made of cheese then basketballs are round,” and “if spiders have eight legs then Sam walks with a limp” are exactly the same. They are both implications: statements of the form, P → Q.

Logical connectives

A Logical Connective is a symbol which is used to connect two or more propositions in such a manner that resultant logic depends only on the input logics and the meaning of the connective used.

Logical Connectives

Let us consider the following two statements:

QUIZ

Logical Connectives

Let us consider the following two statements: P : James bought a shirt and Q : James bought a book.

QUIZ