Propositions are statements that are either true or false. They can be simple or compound.

1. Simple Propositions

A simple proposition is a single statement that cannot be broken into smaller parts.

Examples

1: "The sky is blue"
is a simple statement that is either true or false.

2: "$2+3=5$"
is a single math statement that is true.

2. Compound Propositions

A compound proposition combines two or more simple propositions using logical connectives like:

• and ($\wedge$)
• or ($\vee$)
• not ($\neg$)
• if...then ($\to$)

Examples

1: "The sky is blue and the grass is green."
This combines two simple propositions:

$p:$ "The sky is blue."

$q:$ "The grass is green."

The whole statement is true only if both parts are true.

2: "$2+3=5\wedge 4-1=3$"
This combines two simple math statements:

$p:2+3=5$ (true)

$q:4-1=3$ (true).
into a new statement $p\wedge q$.

The compound statement is true because both parts are true.