1.3 Laws of Formal Logic

 There are two laws of formal logic

1.3.1 Law of Contradiction

It states that the same statement cannot be both true and false

1.3.2 Law of Excluded Middle

It p is a statement then either p is true or p is false and there cannot be a middle ground. If a student appears for the examination of discrete structure then the student will be either pass or fail in that exam. There is no middle stage.

1.4 Connectives and Compound Statements

A statement that cannot be further split into simple sentences is called a primary or primitive or atomic statements.

In day to day life, we use the words NOT, AND, OR, IF-Then, as well as, BUT, WHILE to connect two or more sentences. But these connectives are flexible in their meanings, and lead to inexact and ambiguous interpretations. However, mathematics is a very precise language and every symbol of mathematics has the unique meaning or interpretation in mathematical ocean.

Hence we take some special connectives with precise meaning to suit our purpose. Following are the common connectives with symbols or their rotations.

Sr No

Name of connectives

Symbol

1

Negation

~

2

And (Meet)

^

3

Or (Join)

v

4

If.... then

→

5

If an only if (iff)

↔

1.4.1 Compound Statement

A statement which is formed from primary statements by using logical connectives is called a compound statement.

e.g. If p : I am studying in SE computer class

q : I am learning discrete structure subject

The compound statement is

I am studying in SE computer class and I am learning discrete structure subject.


 


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