Updates

• Changes?• Agenda– Today: Sets– Tomorrow: Venn diagrams– Wed: IB problems– Thurs: Report card pick up– Friday: Project day

Do Now

1. What is the letter symbol for integer, real number, and rationals

2. Find the percent error if the actual is 3.045 and the estimate is 3.

3. What is the symbol for union and intersection, and what does each mean?

Reminder

- Element of:

- Subset of:

- Number of elements:

Practice with Set Builder Notation

Given A = { x| x ϵ Z, 3 < x ≤ 10 }, write down:a. The meaning of the set builder notation.b. List the elements of set Ac. Find n(A)

Compliments of Sets

What is a compliment?

Symbol:

Meaning:

Example

Set U = {1,2,3,4,5,6,7,8,} and A= {1,3,5,7,8}, then A’ =

Note:

A ∩ A’ =

A U A’ =

n(A’) =

ExampleIf U = {x| x ϵ Z, -5≤ x ≤ 5}, A = {x| x ϵ Z, 1≤ x ≤ 4}, B = {x| x ϵ Z, -3≤ x ≤ 2}, List elements in:• A• B• A’• B’• A ∩ B• A U B• A’ ∩ B• A’ U B’

Practice

• If U = {all positive integers}, P = {multiples of 4 less than 50}, Q = {multiples of 6 less than 50}– List P and Q– Find P ∩ Q– Find P U Q– Verify that n(P U Q) = n(P) + n(Q) – n(P ∩ Q)