3-5 Working With Sets

1. 3-5 Working With Sets Objective: To write sets and identify subsets. To find the complement of a set.

2. 3-5 Working With Sets • Set: is a collection of distinct elements • Subset contains elements from a set. • For example: The number 6 on a telephone keypad corresponds to the set { M, N, O}. {M, O} is a subset of that set.

3. 3-5 Working With Sets • You can write sets several ways. • Roster form: { } list elements inside • The set of multiples of 2 is {2, 4, 6, 8, . . . } • Set-builder notation: • {x | x is a multiple of 2} This is read x such that x is a multiple of 2,

4. 3-5 Working With Sets • Example 1: • Write the T is the set of natural numbers that ate less than 6 in roster notation & in set builder notation:

5. 3-5 Working With Sets • Example 2: • In set builder notation write the solution for -5x + 7 ≤ 17

6. 3-5 Working With Sets • Set A is a subset of set B if each element of A is also an element of B. • B = {-2, -1, 0, 1, 2, 3} and A = {-1, 0, 2} • Yes A is a subset of B written: • A  B

7. 3-5 Working With Sets • The empty set or null set is a set with no elements. { } or • Is that the same as {0}?

8. 3-5 Working With Sets • Ex 3: What are all the subsets of {3, 4, 5} • Start with: • List the subsets with one element: • {3} {4} {5} • List the subsets with two elements: • {3, 4} {3, 5} {4, 5} • Use the original, it is also a subset of itself. • {3, 4, 5}

9. 3-5 Working With Sets • The largest set you are working with is the universal set. • The complement of a set is the set of all the elements NOT in the universal set. • The complement of set A is written A’

10. 3-5 Working With Sets • A  U shown below Set A is shaded green: • A’ is shaded green: U U A A

11. 3-5 Working With Sets • Universal set U = {king, queen, bishop, knight, rook, pawn} Look a pic on page 196. • Set A = the set of chess pieces that move side to side. • What is complement of set A:

12. 3-5 Working With Sets • Homework p. 197 9 – 45 every third