Propositional Logic | Propositions Examples

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-

 

 

1. Atomic propositions
2. 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-

1. Command
2. Question
3. Exclamation
4. Inconsistent
5. 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-

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

 

Solutions-

 

1. Proposition (True)
2. Proposition (True)
3. Proposition (False)
4. Not a proposition (Predicate)
5. Proposition (False)
6. Proposition (False)
7. Proposition (False)
8. Proposition (True)
9. Not a proposition (Predicate)
10. Not a proposition (Command)
11. Not a proposition (Question)
12. Not a proposition (Exclamation)
13. Proposition (True)
14. Proposition (True)
15. Not a proposition (Inconsistent)
16. Not a proposition (Command)
17. Proposition (True)
18. Not a proposition (Inconsistent)
19. Proposition (Will be confirmed tomorrow whether true or false)
20. Proposition (True if fan is rotating otherwise false)

 

To gain better understanding about Propositions,

Watch this Video Lecture

 

Next Article- Logical Connectives

 

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