1. 1 Biconditional Statements Define and write biconditionals State the characteristics of good definitions

2. 2 Biconditional Definition When a conditional and its converse are both true, you can combine them A biconditional statement combines the conditional and its converse with the word AND In math, biconditionals are written using IF AND ONLY IF Conditional: If Jen is a member, she has paid her $5 fee. Converse: If Jen has paid her $5 fee, she is a member. Biconditional: Jen is a member if and only if she has paid her $5 fee.

3. 3 Biconditional Example Conditional: If the battery-powered calculator runs, then the batteries are good. Converse: If the batteries are good, then the battery-powered calculator runs. Biconditional: The battery-powered calculator runs if and only if the batteries are good.

4. 4 Separating a Biconditional into Parts Biconditional: A number is divisible by 3 if and only if the sum of its digits is divisible by 3. Conditional: If a number is divisible by 3, then the sum of its digits is divisible by 3. Converse: If the sum of a number’s digits is divisible by 3, then the number is divisible by 3.

5. 5 Characteristics of Good Definitions Uses clearly understood terms Is precise (Avoid sort of, almost, etc.) Is reversible (Can be rewritten as a biconditional)

6. 6 Writing a Definition as a Biconditional Definition: Perpendicular lines are two lines that intersect to form right angles. Biconditional: Two lines are perpendicular if and only if they intersect to form right angles.

7. 7 Examples of Bad Definitions Definition: An airplane is a vehicle that flies. –Not reversible: If a vehicle flies, then it is an airplane. (What about helicopters?) Definition: A triangle has sharp corners. –Not reversible: If a shape has sharp corners, then it is a triangle. (What about a rhombus with sharp corners?)

8. 8 Learning Check and Summary What two things does a biconditional combine? What phrase is commonly used in biconditional statements in math? From a math perspective, why would “A hummingbird is a bird.” be a bad definition?