MATH 11

Math 11 Preparation for the Exam

Set

Well-defined collection of distinct objects, called elements or members

Member

Other term for element

True

A set is a well-defined collection of distinct objects

False

Every set has two or more distinct subsets

True

Sets are usually denoted by capital letters

Roster Method

Lists all elements explicitly

Set-Builder Notation

Describes the property of its members

Cardinality

Number of elements in a set

Finite Set

Having a specific whole number as its cardinality

Symbol for Cardinality

n(A)

False

Zero cannot be used to describe a set’s cardinality

Infinite Set

Infinitely many elements

Infinite Set

Cardinality cannot be expressed by any natural number

False

Natural numbers include 0

False

An infinite set can have a cardinality of zero

Empty Set

A set with a cardinality of zero

Empty set

Set that has no elements

Universal Set

Set containing all elements under consideration for a given context

True

Whole numbers include zero

Set Relations

Describes how two or more sets are connected or compared with each other

Equal Sets

A=B

Equal Sets

Sets that contain exactly the same elements

False

In Equal Sets, order of elements matter

Equivalent Sets

A~B

Equivalent Sets

Sets that have the same number of elements

False

Equivalent sets have the same elements

True

Equal Sets are always equivalent

True

A=C → A~C

False

Equivalent Sets are equal

A~B → A=B

False

True

Equivalent sets are not necessarily equal

True

Equal sets have the same number of elements

False

Equal sets can have the same number of elements but not the same elements

Subset

Every element of A is also an element of B

Superset

Converse of subset

True

Every set is a subset of itself

True

A⊆A

False

The empty set is a subset of every set, except itself

True

∅⊆A ,∅⊆∅

True

The empty set is a subset of every set, including itself

False

A=B if A⊆B

False

Every set is a superset of the empty self, except itself

Proper subset

A is a subset of B, and A is not equal to B

True

Subset allows equality

False

Proper subset allows equality

True

The empty set is a proper subset of every non-empty set

False

∅⊃A

Disjoint Set

Set with no elements in common

Mutually Exclusive sets

Other term for disjoint sets

False

The null set is disjoint with every set except itself

True

The null set is disjoint with every set, including itself

Set Operations

Ways of combining or comparing sets to form new sets

Union

Set of all elements in A or in B

Union

Set of all elements in both A and B

False

A ∪ A = U

True

A∪A = A

True

A∪∅=A

True

A∪U=U

False

A∪B=A if and only if A⊂B

True

A∪B=B if and only if A⊂B

False

A∪B= A or B if A⊂B

True

A∪B= A or B if A=B

Intersection

Set of all elements common to both A and B

Difference

Set of all elements that belong to A but do not belong to B

True

A-B =A and B-A=B if and only if A and B are disjoint

False

If A⊆B, then A-B=A

True

A-B = A∩B’

Complement

Set of all elements in the universal set U that are not in A

False

The complement does not always depend on the universal U

True

A ∪ A’ = U

Cartesian Product

Set of all ordered pairs (a,b)

False

Order doesn’t matter in Cartesian Products

True

A x B is not equal to B x A in general

False

n(A)=m and n(B)=n, then n(AxB) = m+n

True

If A=∅ or B=∅, then A x B = ∅

Power Set

Set of all subsets

False

The null set is not included in the Power set of A, but A is

True

The power set of A also includes the empty set and A itself

True

P(A) always includes the null set and set itself

True

Every s

False

If A⊂B, then A and B may be equal

False

The power set of the null set contains no element

True

The null set is disjoint from every set

True

The null set is disjoint from itself

U

Complement of the null set

A

U ∩ A

A

A U ∅

B. Every set

The null set is a subset of:

8

if A={1,2,3}, then how many elements does P(A) have?

U-A

The complement of Set A is:

(A∩B) ∪ (A∩C)

A ∩ (B∪C) is equal to

Subsets of A: ∅, {1},{2},{1,2}

What are the subsets of A={1,2}