Mathematical Logic- Intro
• In this chapter we shall study mathematical logic, which is concerned with
all kinds of reasoning
• Mathematical logic has two aspects
On one hand it is analytical theory of art of reasoning whose goal is to
systematize and codify principles of valid reasoning. It may be used to judge the
correctness of statements which make up the chain. In this aspect logic may be
called ‘classical’ mathematical logic
The other aspect of Mathematical logic is inter-related with problems relating the
foundation of Mathematics.
Principles of logic are valuable to problem analysis, programming and logic
design.
,Statement
A statement is a declarative sentence which is either true or false but not both. The truth or
falsity of a statement is called its truth value. The truth values ‘True’ and ‘False’ of a statement
are denoted by T and F respectively. They are also denoted by 1 and 0.
, Connectives & Compound Statements
Statements can be connected by words like ‘not’, ‘and’, etc. These words are
known as logical connectives.
The statements which do not contain any of the connectives are called atomic
statements or simple statements.
A statement that is formed from atomic (Primary) statements through the use of
sentential connectives is called a compound statement.
The common connectives used are:
negation (~) [or (￢)],
and (∧)
or (∨),
if ... then (→),
if and only if (↔),
equivalence (≡) or (⇔). We will use these connectives along with symbols to
combine various simple statements.
• In this chapter we shall study mathematical logic, which is concerned with
all kinds of reasoning
• Mathematical logic has two aspects
On one hand it is analytical theory of art of reasoning whose goal is to
systematize and codify principles of valid reasoning. It may be used to judge the
correctness of statements which make up the chain. In this aspect logic may be
called ‘classical’ mathematical logic
The other aspect of Mathematical logic is inter-related with problems relating the
foundation of Mathematics.
Principles of logic are valuable to problem analysis, programming and logic
design.
,Statement
A statement is a declarative sentence which is either true or false but not both. The truth or
falsity of a statement is called its truth value. The truth values ‘True’ and ‘False’ of a statement
are denoted by T and F respectively. They are also denoted by 1 and 0.
, Connectives & Compound Statements
Statements can be connected by words like ‘not’, ‘and’, etc. These words are
known as logical connectives.
The statements which do not contain any of the connectives are called atomic
statements or simple statements.
A statement that is formed from atomic (Primary) statements through the use of
sentential connectives is called a compound statement.
The common connectives used are:
negation (~) [or (￢)],
and (∧)
or (∨),
if ... then (→),
if and only if (↔),
equivalence (≡) or (⇔). We will use these connectives along with symbols to
combine various simple statements.
