Logic

→ Logic:-

• Logic came from the Greek word logos, means “discourse”, “reason”.

• It is defined as the study of the principles of correct reasoning.

→ Types of Logic:

1. Propositional Logic
2. 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.

1. 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.

Note: In propositional logic, there are two types of sentences:

• Simple Sentence
• Compund Sentence

→ 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.”

→ Compund 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.