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

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

- well defined

- not well defined

- not well defined

Symbols related to sets:Symbol Term

or { } empty set

in

not in

n(A) number

Symbols related to sets:Term Symbol Read as

union or

intersection and

complement not (in A)

subset A

Given the sets U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9},A = {0, 2, 4, 5, 6, 8}, andB = {1, 3, 5, 7}Answer the questions below:

•Find n(B).

•Find the set A B.

•Find the set

n(B) = 4

= {0, 2, 4, 6, 8, 9}

A B = {5}These are the things that are in set A and also in set B at the same time.These are the things that are in set U (the universe for our problem) that are not in set B.

B B

Given the sets U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9},A = {0, 2, 4, 5, 6, 8}, andB = {1, 3, 5, 7}Answer the questions below:•Find the set .

•Is 7A true or false?

•Is 5B true or false?

BA

Cardinal Number Formula for the Union of Sets

n(AB) = n(A) + n(B) — n(AB)

Formulas

Cardinal Number Formula for the Complement of a Set

)()()( AnAnUn

If n(AB) = 40, find n(AB) and draw a Venn diagram to illustrate the composition of U.

Suppose n(U) = 61, n(A) = 32, and n(B) = 26.

n(AB) = n(A) + n(B) — n(AB)

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)

1.Draw a Venn diagram illustrating the results of the survey.

2.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.