MAT 142 Lecture Video Series

Sets and Set Operations Sets and Set Operations (MAT 142) Sets and Set Operations

Objectives Determine if a set is well defined. Write all the subsets of a given set and label the subsets as proper or improper. Given a universal set and some subsets, find a complement, intersection or union. Draw a Venn diagram to illustrate two sets. Use the cardinal number formula.

Vocabulary roster notation set-builder notation well defined set cardinal number empty set subset proper/improper subset intersection of sets union of sets mutually exclusive complement of a set

Set Vocabulary: roster notation: set builder notation: a complete or implied listing of all the elements of the set set builder notation: used when the roster method is cumbersome or impossible

Set Vocabulary: well defined set: A set is well-defined if any given object either is an element of the set, or is not an element of the set

Determine if the given set is well defined. The set of all good bands The set of odd numbers The set of small numbers - not well defined - well defined - not well defined

Sets and Set Operations (MAT 142) Symbols related to sets: Symbol Term  or { } empty set  in  not in n(A) number

Sets and Set Operations (MAT 142) Symbols related to sets: Term Symbol Read as union  or intersection  and complement  not (in) subset 

Given the sets U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {0, 2, 4, 5, 6, 8}, and B = {1, 3, 5, 7} Answer the questions below: Find n(B). Find the set A  B. Find the set B  n(B) = 4 A  B = {5} These are the things that are in set A and also in set B at the same time. B’ = {0, 2, 4, 6, 8, 9} These are the things that are in set U (the universe for our problem) that are not in set B.

Sets and Set Operations (MAT 142) Given the sets U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {0, 2, 4, 5, 6, 8}, and B = {1, 3, 5, 7} Answer the questions below: Find the set A  B. Is 7A true or false? Is 5B true or false?

Formulas Cardinal Number Formula for the Union of Sets n(AB) = n(A) + n(B) — n(AB) Cardinal Number Formula for the Complement of a Set n(U) = n(A) + n(A )

Suppose n(U) = 61, n(A) = 32, and n(B) = 26. If n(AB) = 40, find n(AB) and draw a Venn diagram to illustrate the composition of U. n(AB) = n(A) + n(B) — n(AB)

In a recent health survey, 750 single men in their twenties were asked to check the appropriate box or boxes on the following form. I am a member of a private gym. I am a vegetarian. The results were tabulated as follows: 374 checked the gym box 92 checked the vegetarian box 332 were blank (no boxes checked)

750 men surveyed 374 checked the gym box 92 checked the vegetarian box 332 were blank (no boxes checked) Draw a Venn diagram illustrating the results of the survey. What percent of these men were both members of a private gym and vegetarians.

Cards

Cards Determine how many cards, in an ordinary deck of 52, are clubs or twos.

Cards Determine how many cards, in an ordinary deck of 52, are face cards or diamonds.

Cards Determine how many cards, in an ordinary deck of 52, are threes or sixes.

Cards Determine how many cards, in an ordinary deck of 52, are threes and sixes.

Creator and Producer Elizabeth Jones for The School of Mathematical and Statistical Sciences at Arizona State University Videographer Mike Jones ©2009 Elizabeth Jones and School of Mathematical and Statistical Sciences at Arizona State University