propositional logic


Propositions : A proposition is a declarative sentence that is either true or false but not both.Example-

1 . A week has seven days.

2.Parrot is the smallest bird.

3.1+1=2

4.2+2=5

Here 1 and 3 is true . but 2 and 4 are false. So these sentences are propositions. Some sentences are not proposition. Example –

1.what is your name?

2 . x + 1=2

3.Read Carefully.

4.x+y=z

These sentence are not proposition because they are not declarative sentences.

Propositional Logic : The area of logic that deals with proposition is called the propositional calculus or propositional logic.

Compound Proposition : New proposition is called compound propositions are formed from existing propositions using logical operations.

Excercise -1 :

Find the negation of the proposition ” It’s 10 AM now.  ”

Solve:

It is not the case that it is 10 AM now.

or It’s not 10 AM now.

Excercise – 2 :

Find the Negation of the proposition ” At least 10 inches of rain fell today in Miami. ”

Solve :

It is not the case that at least 10 inches of rain fell today in Miami.

or Less then 10 inches of rain fell today in Miami.

Truth – Table :

The logical operators that are used to form a new propositions from two or more existing propositions are called connectives.

p ¬p
T F
F T

Read more in part – 2…

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