6.1 Sets and Set Operations Day 2 Turn to page 276 and look at example 6.

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Presentation transcript:

6.1 Sets and Set Operations Day 2 Turn to page 276 and look at example 6

Set Union: Let A and B be sets. The union of A and B, written is the set of all elements that belong to either A or B. Set Intersection: Let A and B be sets. The intersection of A and B, written is the set of all elements that are common to A and B. Set Operations

Ex. Given the sets: Combine the sets Overlap of the sets

Venn Diagrams U AB – visual representation of sets Rectangle = Universal Set Sets are represented by circles

Venn Diagrams U AB C A C B U These are all shaded the same in all parts.

Let A ={1,3,5,7} and B ={2,4,6} Find A∩B A∩B=Ø If two sets have nothing in common (aka the intersection is the empty set) then the sets are said to be DISJOINT

Complement of a Set: If U is a universal set and A is a subset of U, then the set of all elements in U that are not in A is called the complement of A, written A C. Set Complementation

Ex. Given the sets: Elements not in A. Elements in A and not in B.

Venn Diagrams U A AB U

Let U denote the set of all cars in a dealer’s lot and A= {x  U | x is equipped with automatic transmission} B = {x  U | x is equipped with air conditioning} C = = {x  U | x is equipped with power steering} Find an expression in terms of A, B, and C for each of the following sets: a. The set of cars with at least one of the given options. b. The set of cars with exactly one of the given options. c. The set of cars with auto trans and pow steer, but no AC a. A  B  C b. Auto trans only is A  B c  C c and AC only is B  C c  A c and Pow Steer only is C  A c  B c so the set of all three gives us (A  B c  C c)  (B  C c  A c )  (C  A c  B c ) c. A  C  B c

Shade in the portion of the figure that represents the given set. A B U First we put a dot in Then we put a dot in We are doing intersection so we look for the parts that have 2 dots and shade there.

A B U C Shade in the portion of the figure that represents the given set. This is So this is the complement Now we add dots to A To do union we color everywhere there are dots (no matter how many there are) and get this…

Homework #1 P – 20 all #2 P – 47 odd