**→ 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**:

- 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.

**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.