Deductive Versus Inductive Reasoning

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 Term Symbol Read as  set-builder notation union  well defined set intersection  cardinal number complement  empty set subset  subset  proper/improper Cardinal Number Formula for Union of subset Sets:  intersection of sets  union of sets  mutually exclusive Cardinal Number Formula for Complement  complement of a set of a Set:

Symbol Term empty set in not in number

Sets and Set Operations Page 1 of 3 Possible Classroom Examples:

Is the given set well-defined?  the set of all pink automobiles  the set of all good bands  the set of odd numbers  the set of small numbers

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, 9}  Find n(B).  True or false: 7  A  True or false: 5  B  A  B A  B  B  A  B

Suppose n(U) = 61, n(A) = 32, n(B) = 26.  If n(AB) = 40, find n(AB) and draw a Venn diagram illustrating the composition of U n(A  B)  40 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, and 332 were blank (no boxes checked). a. Draw a Venn diagram illustrating the results of the survey. b. What percent of these men were both members of a private gym and vegetarians?

Sets and Set Operations Page 2 of 3 Determine how many cards, in an ordinary deck of 52, fit the description. a. clubs or twos b. face cards or diamonds c. threes or sixes d. threes and sixes

Deck of Cards Hearts – Red Diamonds – Red

Clubs – Black Spades – Black

Sets and Set Operations Page 3 of 3