What Are Propositions?

A proposition is a statement that can be clearly classified as true or false. In symbolic logic, we use letters like \( p \), \( q \), or \( r \) to represent propositions.

Logical Connectives

Logical connectives help us build complex statements from simpler ones. The main connectives are:

• Conjunction (\(\land\)): Both must be true (e.g., "It is raining and cold").
• Disjunction (\(\lor\)): At least one must be true (e.g., "It is raining or snowing").
• Negation (\(\lnot\)): Flips the truth value (e.g., "It is not raining").
• Implication (\(\rightarrow\)): If one, then the other (e.g., "If it rains, then the ground is wet").
• Biconditional (\(\leftrightarrow\)): Both must be the same (e.g., "The light is on if and only if the switch is up").

Combining Propositions

You can build complex logical statements using these connectives, making reasoning more precise.

Truth Tables

Truth tables show all possible truth values of compound statements, helping you see how logical connectives work.

Sample Truth Table for Conjunction