Conditional and Biconditional Statements

Conditional and Biconditional Statements in Logic

1. Conditional Statement

A conditional statement expresses a relationship between two propositions where one depends on the other. It is often written in the form:
“If $P$, then $Q$“

• Symbolically: $P\to Q$
• Read as: “If $P$, then $Q$.”

Examples:

• If it rains, then the ground will be wet.
• If a number is even, then it is divisible by 2.

Truth Table:

2. Biconditional Statement

A biconditional statement expresses a relationship where both propositions are mutually true. It is often written as:
“If and only if $P$, then $Q$“

• Symbolically: $P\leftrightarrow Q$
• Read as: “$P$ if and only if $Q$.”

Examples:

• A figure is a square if and only if it has four equal sides and four right angles.
• You will pass the exam if and only if you score at least 50%.

Truth Table:

Key Differences