Warm Up 1.Let p = Today is your birthday, and q = You will have cake. Write p => q in words. Write p => q in words. 2. Write the converse of the statement: “You need to get good grades in high school if you want to go to college.” “You need to get good grades in high school if you want to go to college.”

Lesson 2-4 Good Definitions

2-4 Good Definitions Good Definitions must: I. Include words commonly understood (known terms) II. Accurately describe the idea ( be accurate) III. Include no more information than is necessary (be concise).

The midpoint of a segment AB is the point M on AB with AM = MB. A MB What is a good definition of a midpoint?

Bad Definitions The Midpoint of a segment is a point between the endpoints. Violates Property #________

Bad Definitions The midpoint M of AB is the point M on AB between A and B, the same distance from A and B, so that MA = MB Violates Property #______

Bad Definitions The Midpoint M of AB is the intersection of AB and a bisector of AB Violates Property #______

The midpoint of a segment AB is the point M on AB with AM = MB Conditional: If M is the midpoint of AB, then M is on AB and AM = MB. term => characteristics Converse: If M is on AB and AM = MB, then M is the midpoint of AB. characteristics => term **M is the midpoint of AB if and only if M is on AB and AM = MB.**

A good definition consists of a true conditional and its converse. p => q and q => p are both true Bi-conditional p  q “p if and only if q” abbreviated: p iff q Every good definition can be written as a bi-conditional.

Example 1 If a polygon has eight sides then it is an octagon. Converse: If a polygon is an octagon, then it has eight sides. Bi-conditional: A polygon has eight sides iff it is an octagon.

Example 2 If a network is traversable then it has two or less odd nodes. Converse: If a network has two or less odd nodes, then it is traversable. Bi-conditional: A network is traversable if and only if it has two or less odd nodes.

A circle is the set of all points in a plane at a certain distance (its radius) from a certain point (its center).

Homework, Part I: Pages 84-86: 1-13, 16-19

Section 2.5 Unions and Intersections of Figures

Who plays in what group? Choir: Band: C ∩ B: (intersection- in common)

Union C U B = in Choir or Band C U B =

The Null Set or Empty Set

Classifying Vehicles

Which vehicles are cars and which vehicles are not cars

Which vehicles are cars and which vehicles are green

Let C = x > 2 and D = x 2 and D = x < 7 a.Describe C U D b. Describe C ∩ D

Let E = rectangle PQRS and let F = PR U QS 1.Draw E 2.Draw F 3.E U F 4.E ∩ F