Proposition

Definition

A proposition is a statement that can be true or false.

Example:

2 + 3 = 5

This is a proposition because it has a truth value.

It is true.

Another example:

2 + 3 = 9

This is also a proposition.

It is false.

Proposition = statement with a truth value.

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Not Every Sentence Is A Proposition

Some sentences are not propositions.

Question:

What time is it?

Command:

Close the door.

Expression:

x + 1

These are not propositions because they are not true or false by themselves.

A proposition must be capable of truth or falsity.

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Proposition Symbols

Logic often uses symbols to represent propositions.

Example:

P = "It is raining"
Q = "The ground is wet"

Then we can reason with:

P
Q
P AND Q

The symbols let us focus on structure.

Proposition symbols stand for full statements.

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Atomic And Compound Propositions

An atomic proposition is not built from smaller logical parts.

Example:

P

A compound proposition combines propositions using logical operators.

Example:

P AND Q

The compound statement's truth depends on the truth of its parts.

Compound propositions are built from simpler propositions.

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Why Propositions Matter

Reasoning needs statements that can be evaluated.

Example:

If P is true, and P implies Q, then Q is true.

This only works because P and Q are propositions.

They can be true or false.

Propositions are the basic truth-bearing units of logic.

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Final Summary

• A proposition is a statement that can be true or false.
• Questions, commands, and incomplete expressions are not propositions.
• Proposition symbols can stand for full statements.
• Atomic propositions are basic statements.
• Compound propositions are built using logical operators.
• Propositions are the basic units used in logical reasoning.