Math 1100 - 2.1, 2.2, 2.3, 2.4

to determine the number of proper subsets 2^n-___.

1

To determine the number of subsets...

2^n

Determine how many regions the universal set will be divided into when there is a Venn diagram with three sets.

8 regions

intersection

A point where lines intersect.

Let U​ = {​ 1, 2,​ 3, . . .​ }, A​ = { 3, 6​, 9​, . . .​ }. Use the roster method to write the set A'.

A' =​ {1, 2, 4, 5, 7, 8​, . . .​ }

Find the set A union B. U = {1, 2, 3, 4, 5, 6, 7} A = {1, 2, 4, 6} B = {3, 4, 5}

AUB = {1,2,3,4,5,6}

Find the set (A intersect(n) B) U = {1, 2, 3, 4, 5, 6, 7, 8, 9} A = {1, 2, 3, 5} B = {1, 2, 4}

AnB= {1,2}

equal set if A=B the set A contains exactly the same elements as set ___.

B

subset.....

C (underlined)

Describe a universal set U that includes all elements in the given sets. A=​{geometry. biology​} B=​{literature} A. the set of all sciences B. the set of the elements geometry, and literature C. the set of all school subjects D. the set of teachers

C. the set of all school subjects

Let C= {f,m,g,c,s}. Find C union empty set.

CU0/ = {f, m, g, c, s}

Venn _________ are pictures - visuals - of set and set operations.

Diagrams

___________ sets are sets that have no elements in common. In a Venn​ diagram, sets are represented by shapes.

Disjoint

The symbol ___ is an element of {} is used to indicate that an object is an element of a set. To say that x is an element of A is to say that x is an element of the set A.

E

(T or F) As the number of elements in a set​ increases, larger circles are needed to represent the set.

False, the size of a circle does not need to be proportional to the number of elements in its corresponding set.

an empty set is represented by...

O with a / through it

proper subsets...

Set A is a proper subset of set B, denoted ⊂ B m if every element of A is an element of B, and A ≠ B.

(T or F) If set A is a proper subset of set​ B, the sets are represented by two circles where circle A is drawn outside of circle B.

The statement is false. If set A is a proper subset of set​ B, the sets are represented by two circles where circle A is drawn inside of circle B.

(T or F) Disjoint sets are represented by circles that do not overlap.

True

(T or F) Equal sets are represented by the same circle.

True

define a set

an unordered, distinct, objects... {1,2,3.}

the infinite set of natural numbers {1,2,3,4,5,6, ...} is called a transfinite ________ number (N0).

cardinal

sets and their visual representation help organize. describe and _______ data.

classify

The set of all elements in the universal set that are not in set A is called the​ _________ of set​ A, and is symbolized by​ _________.

complement / A'

each item in a set is considered an _______________.

element (E)

some common elements... overlaping __________.

elements

the three dots after an element is called an...

ellipsis

The statement empty set is a subset of B tells us that the ________ set is a subset of every set.

empty

a __________ set or null _______ set is the set that contains no elements.

empty/set

A U B are not _____.

equal

Think of a subset as "less than or _______ to" in arithmetic.

equal

Two sets that contain the same elements are called ___________ sets.

equal

Two sets that contain the same number of elements are called​ _______.

equivalent

A statement is a sentence that is either true or​ ________, but not both simultaneously.

false

the negation of a true statement is a _______ statement and the negation of a false statement is a true statement.

false

an ___________ set, such a as a set of natural numbers can be defined as any set that can be placed in a one-to-one correspondence with a a proper subset of itself.

infinite

For set​ operations, always begin by performing any operations _________ the parentheses.

inside

In order to perform set operations such as left parenthesis Upper A union Upper B right parenthesis intersect left parenthesis Upper A union Upper C right parenthesis​, begin by performing any set operations​ ________.

inside the parenthesis

The set of elements common to both set A and set B is called the ______________ of sets A and​ B, and is symbolized by Upper A intersect Upper B.

intersection

E means....

is an element of.

Consider then a proper subset as strictly ________ than in arithmetic.

less

The formula for the cardinal number of elements in set A or set B is n left parenthesis Upper A union Upper B right parenthesis equals​________.

n(A)+n(B)-n(AnB)

The set of counting​ numbers, {1, 2, 3, 4, 5,...} also called the set of ____________ numbers, is represented by the boldface letter N.

natural​

the notation A U/ B means A is not a ________ subset of B.

not

C means is a subset ___.

of

The number of distinct ________ subsets of a set with n elements is 2 Superscript n Baseline minus 1.

proper

the empty set is a _______ subset of every set except for itself.

proper

Statements that contain the words all​, some​, and no are called __________statements.

quantified

The set​ {California, Colorado,​ Connecticut} is expressed using the _____________ method. The set​ {x|x is a U.S.state whose name begins with the letter​ C} is expressed using __________ notation.

roster / set-builder

a subset is itself a _______.

set

every _____ is a subset of itself...

set

disjoint _______ are two sets that have no elements in common.

sets

The circles that represent a set do not need to be proportional to the ______ of the corresponding set.

size

A set cannot be a proper _______ of itself.

subset

The empty set is a proper ________ of every other set!

subset

Cardinality is....

the number of elements in a set

disjoint sets...

there is no relationship between sets.

Determine if the following statement is true or false. It can be proved that, (A n B)' = A' U B' so this means that the complement of the intersection of two sets is the union of the complement of those sets.

true. The statement is true because a theorem is always true and means that the complement of the intersection of two sets is the union of the complement of those sets.

The set of elements that are members of set A or set B or of both sets is called the​ _________ of sets A and​ B, and is symbolized by​ _________.

union/AUB

a ____________ set contains all elements in a given discussion or problem. (U)

universal

naming a set....

use capital letters

a ___________ diagram are used to show a relationship between sets.

venn

The negation of a statement p is expressed by writing ____. This is read as​ "not p​" or​ "It is not true that p​."

​~p