Logic came from the Greek word logos, means “discourse“, “reason“.
Thank you for reading this post, don't forget to subscribe!- It is defined as the study of the principles of correct reasoning.
Types of Logic:
- Propositional Logic
- Predicate Logic
Note:
A proposition is a declarative sentence which is either true or false but not both. A sentence which is both true and false is called a paradox. Paradox is not a statement.
example:
- 2+2=5 (false), It is a proposition.
- kathmandu is the capital city of Nepal. (True), It is a proposition.
- Open the door. It is not a proposition.
Note: x>15, go there, who are you?
The above mentioned sentences are not propositions since we cannot say whether they are true or false.
Propositional variable:-
Propositional variables (also called propositional symbols or atomic propositions) represent simple statements that can be either true or false.
- It is the placeholders for proposition. Propositional variable is denoted by letter p, q, r etc.
Propositional Logic:
Propositional Logic is the branch of logic that studies way of joining or modifying propositions to form more complicated propositions as well as logical relationship.
• It is also know as sentential logic/statement logic.
In propositional logic, there are two types of sentences:
- Simple Sentence
- Compund Sentence
1.) Simple Sentence:
Simple sentences are basic statements that cannot be further divided into simpler statements.
- It also known as atomic sentences or atomic propositions.
Examples:
- “The sun rises in the east.”
- “Water boils at 100 degrees Celsius.”
- “Elephants are the largest land animals.”
- “Paris is the capital of France.”
2.) Compound Sentence:
A compound sentence is a sentence that is formed by combining two or more simple sentences using logical connectives (such as conjunction, disjunction, implication, etc.)
examples:
- “It is raining AND the grass is wet.”
- “It is raining OR it is snowing.”
- “If it is raining, then the ground is wet.”
Simple proposition:
Any statement whose truth value does not depend on another proposition is called simple proposition.
- Example: Kathmandu is the capital city of Nepal.