Chapter 2 Test Review (The nature of sets)

Union of sets

A set containing all elements of all sets being considered.

Intersection of sets

A set containing elements in common for all sets being considered.

Set of Natural Numbers

N = {1,2,3,4,5,6,7,8, ...}

Set

A collection of objects and things

Venn Diagram

A diagram that consists of Universal set U represented by a rectangle and uses circles to display elements of different sets.

Not an Element of

Not a member of set A.

Elements of a set

Objects or members which make up the set

Intersection

Objects that belong to set A and set B

Union

Objects that belong to set A or set B

Equal sets

Set A & set B contain the same elements.

Subset

Set A is a _______ of set B if and only if every element of set A is in set B.

Set of Rational Numbers

Set of any number that can be expressed as a fraction where p and q are integers and q does not equal zero.

Disjoint sets

Sets that do not have any elements in common

Set of Whole Numbers

W = {0,1,2,3,4,5,6,7,8, ...}

Set of Integers

Z = {... -4,-3,-2,-1,0,1,2,3,4, ...}

If A = {1, 3, 5, 7} and C = {2, 4, 6, 8}, then A ∪ C

{1, 2, 3, 4, 5, 6, 7, 8}

If A = {1, 3, 5, 7} and B = {3, 5, 7, 8}, then A ∪ B

{1, 3, 5, 7, 8}

If B = {3, 5, 7, 8} and C = {2, 4, 6, 8}, then B ∪ C

{2, 3, 4, 5, 6, 7, 8}

If A = {1, 3, 5, 7} and B = {3, 5, 7, 8}, then A ∩ B

{3, 5, 7}

If A = {1, 3, 5, 7}, B = {3, 5, 7, 8}, and C = {2, 4, 6, 8}, then (A ∩ B) ∪ (A ∩ C)

{3, 5, 7}

If A = {1, 3, 5, 7}, B = {3, 5, 7, 8}, and C = {2, 4, 6, 8}, then (A ∪ B) ∩ C

{8}

If A = {1, 3, 5, 7}, B = {3, 5, 7, 8}, and C = {2, 4, 6, 8}, then A ∩ B ∩ C

∅

Intersection Symbol

∩

Union Symbol

∪

Null or Empty Set

The set does not contain any elements.

Complement

The set of all elements of Universal set which are not elements of set A.

Universal Set

The set of all possible elements.