Set Notation 1.3 – 1.4 Quiz Topics - Use set notation to list all elements of a set. - Determine whether a set is well defined. - Decide whether a pair of sets are equal. - Decide whether a pair of sets are equivalent. - Decide if a subset is proper or not. - Define the five number sets we already know.

Class work/Homework Page 66 – 67 Problems 1 - 19

1.5 Set Operations Perform the set operations of union, intersection, complement, and difference on sets. Use Venn diagrams to illustrate set operations. Understand how to determine n(A  B).

We form the union of sets by joining sets together. The union of sets A and B, written A  B, is the set of elements that are members of either A or B (or both). Using set-builder notation: A  B = {x:x is member of A or x is a member of B} The union of more than two sets is the set of all elements belonging to at least one of the sets.

The intersection of sets is the set of elements they have in common. The intersection of sets A and B, written A  B, is the set of elements common to both A and B. Using set-builder notation: A  B = {x:x is a member of A and x is a member of B} The intersection of more than two sets is the set of elements that belong to each of the sets. If A  B =Ø, then we say that A and B are disjoint.

The elements not in a set form its complement. If A is a subset of the universal set U, the complement of A is the set of elements of U that are not elements of A. This set is denoted by A`. Using set-builder notation: A` = {x:x  U, but x  A}

To form a set difference, begin with one set and remove all elements that appear in a second set. The difference of sets B and A is the set of elements that are in B but not in A. This set is denoted by B – A. Using set-builder notation: B – A = {x:x is a member of B and is not a member of A}.

Set operations must be performed in correct order. Make sure to solve inside the parentheses first. DeMorgan’s Laws for Set Theory If A and B are sets, then (A  B)` = A` B` If A and B are sets, then (A  B)` = A` B` We can use the Three-Way Principle in deciding whether a set property holds true. Verbally (describe the situation verbally) Graphically (draw Venn diagrams) Examples (use sets of numbers)

The Cardinal Number of the Union of Two Sets If A and B are sets, then n(A  B) = n(A) + n(B) – n(A  B)

Classwork/Homework Classwork – Page 51(11 – 17 odd, 23, 25, 29 – 33 odd, 43, 77) Homework – Page 51 (12 ,14, 18, 24, 30, 32, 78, 80, 82)

Homework Sets 11 – 17 odd U = {1,2,3,…,10} A = {1,3,5,7,9} B = {1,2,3,4,5,6} C = {2,4,6,7,8}

Homework Sets 23, 25 E = {x:x will use computer for education} B = {x:x will use computer for business} H = {x:x will use computer for home mgt}

Homework Sets 29 - 33 U = {apple, TV, hat, radio, fish, sofa, automobile, potato chip, bread, banana, hammer, pizza} M = {x:x is human-made} E = {y:y is edible} G = {t:t grows on a plant}

Classwork/Homework Classwork – Page 51 (19, 21, 33, 35, 37, 45, 51 – 57 odd, 81, 83) Homework – Page 51 (20, 22, 26, 34, 36, 38, 46, 52 – 58 even)