**Propositions-**

In propositional logic,

- Proposition is a declarative statement declaring some fact.
- It is either true or false but not both.

**Propositions Examples-**

The examples of propositions are-

- 7 + 4 = 10
- Apples are black.
- Narendra Modi is president of India.
- Two and two makes 5.
- 2016 will be the lead year.
- Delhi is in India.

Here,

- All these statements are propositions.
- This is because they are either true or false but not both.

**Types Of Propositions-**

In propositional logic, there are two types of propositions-

- Atomic propositions
- Compound propositions

**1. Atomic Propositions-**

- Atomic propositions are those propositions that can not be divided further.
- Small letters like p, q, r, s etc are used to represent atomic propositions.

**Examples-**

The examples of atomic propositions are-

- p : Sun rises in the east.
- q : Sun sets in the west.
- r : Apples are red.
- s : Grapes are green.

**2. Compound Propositions-**

- Compound propositions are those propositions that are formed by combining one or more atomic propositions using connectives.
- In other words, compound propositions are those propositions that contain some connective.
- Capital letters like P, Q, R, S etc are used to represent compound propositions.

**Examples-**

- P : Sun rises in the east and Sun sets in the west.
- Q : Apples are red and Grapes are green.

**Statements That Are Not Propositions-**

Following kinds of statements are not propositions-

- Command
- Question
- Exclamation
- Inconsistent
- Predicate or Proposition Function

**Examples-**

Following statements are not propositions-

- Close the door. (Command)
- Do you speak French? (Question)
- What a beautiful picture! (Exclamation)
- I always tell lie. (Inconsistent)
- P(x) : x + 3 = 5 (Predicate)

**PRACTICE PROBLEMS BASED ON PROPOSITIONS-**

Identify which of the following statements are propositions-

- France is a country.
- 2020 will be a leap year.
- Sun rises in the west.
- P(x) : x + 6 = 7
- P(5) : 5 + 6 = 2
- Apples are oranges.
- Grapes are black.
- Two and two makes 4.
- x > 10
- Open the door.
- Are you tired?
- What a bright sunny day!
- Mumbai is in India.
- I always tell truth.
- I always tell lie.
- Do not go there.
- This sentence is true.
- This sentence is false.
- It will rain tomorrow.
- Fan is rotating.

**Solutions-**

- Proposition (True)
- Proposition (True)
- Proposition (False)
- Not a proposition (Predicate)
- Proposition (False)
- Proposition (False)
- Proposition (False)
- Proposition (True)
- Not a proposition (Predicate)
- Not a proposition (Command)
- Not a proposition (Question)
- Not a proposition (Exclamation)
- Proposition (True)
- Proposition (True)
- Not a proposition (Inconsistent)
- Not a proposition (Command)
- Proposition (True)
- Not a proposition (Inconsistent)
- Proposition (Will be confirmed tomorrow whether true or false)
- Proposition (True if fan is rotating otherwise false)

To gain better understanding about Propositions,

**Next Article-****Logical Connectives**

Get more notes and other study material of **Propositional Logic**.

Summary

Article Name

Propositional Logic | Propositions Examples

Description

In propositional logic, propositions are the statements that are either true or false but not both. Examples of Propositions. Types of Propositions- Atomic Proposition and Compound Proposition.

Author

Akshay Singhal

Publisher Name

Gate Vidyalay

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