Propositions and Compound Statements in Logic: Building Logical Expressions

Learn about propositions (declarative statements with truth values) and how to construct compound statements using logical connectives (AND, OR, NOT, etc.). This guide explains the basic building blocks of logic and how to analyze the truth values of compound statements.

Propositions and Compound Statements in Logic

What is a Proposition?

A proposition is a declarative sentence (a statement) that is either definitively true or definitively false. It's a statement that can have a truth value assigned to it (true or false).

Examples of Propositions

• The Earth is round. (True)
• 2 + 2 = 5. (False)
• The sky is blue. (It depends on the context and time; this would need more information to be definitively true or false)

Examples of Non-Propositions

• What time is it?
• Close the door.
• x + 2 = 5

(The last example is not a proposition because its truth depends on the value of x.)

Propositional Variables

In logic, we often use lowercase letters (typically starting from p) to represent propositions. For example:

• p: It is raining.
• q: The ground is wet.

Compound Statements

Compound statements are formed by combining simple propositions using logical connectives (also called logical operators).

Logical Connectives

Conclusion

Propositions and compound statements are fundamental building blocks of logic. Understanding how to represent and combine propositions using logical connectives is essential for reasoning and building more complex logical arguments.