Math 105
And
Intersection
Roster form
Listing the elements of a set inside a pair of braces, { }, is called roster form.
To Change a Decimal Number to a Percent
Multiply the decimal number by 100. Add a percent sign.
Proper subsets
Set A is a proper subset of set B, symbolized A ⊂ B, if and only if all of the elements of set A are elements of set B and set A ≠ B (that is, set B must contain at least one element not is set A).
Subsets
Set A is a subset of set B, symbolized A ⊆ B, if and only if all elements of set A are also elements of set B. •The symbol A ⊆ B indicates that "set A is a subset of set B."
Equal sets
Set A is equal to set B, symbolized by A = B, if and only if set A and set B contain exactly the same members.
Cardinal number
The cardinal number of set A, symbolized n(A), is the number of elements in set A.
Describe what is meant by the complement of a set?
The complement of set A is the set of all elements in the universal set that are not in A. This is symbolized by A'.
Intersection
The intersection of sets A and B, symbolized A ∩ B, is the set containing all the elements that File are common to both set A and set B. •Region II represen
Number of Distinct Proper Subsets
The number of distinct proper subsets of a finite set A is 2n - 1, where n is the number of elements in set A.
Number of distinct subsets
The number of distinct subsets of a finite set A is 2n, where n is the number of elements in set A.
Inductive reasoning
The process of reasoning to a general conclusion through observations of specific cases. Also called induction Example: every quiz has been easy therefore the test will be easy
How is symbol E read
The symbol ∈, read "is an element of," is used to indicate membership in a set. •The symbol ∉ means "is not an element of."
What is the symbol for a universal set and what does it mean?
U; contains all of the elements for any specific discussion it will always contain the word or in it.
Or
Union
How would you find the the union of A u B'
You are looking for the elements that are members of set A or set B or both sets.
Complement of set A
symbolized A, is the set of all elements in the universal set that are not in set A.
Venn Diagram
A Venn diagram is a useful technique for illustrating set relationships. •Named for John Venn.
A proper subset is symbolized like a "c"
All the elements of set A are elements of set B.
deductive reasoning
Also called deduction. Deductive reasoning is the process of reasoning to a specific conclusion from a general statement. Example: geometric proof
set-builder notation
A formal statement that describes the members of a set is written between the braces. •A variable may represent any one of the members of the set. Example:
Set
A set is a collection of objects, which are called elements or members of the set. •Three methods of indicating a set: •Description •Roster form •Set-builder notation
When is a set well defined
A set is well defined if its contents can be clearly defined.
Finite set
A set that contains no elements or the number of elements in the set is a natural number. It has a beginning and an ending
Two sets with no elements in common are called ________ sets.
Disjoint
The set of elements common to both set A and B is called the ________ of sets A and B, and is symbolized by ______?
Intersection; AnB Set builder notation is AnB= {x|xEA and xEB}
To Change a Percent to a Decimal Number
Divide the number by 100. Remove the percent sign.
To Change a Fraction to a Percent
Divide the numerator by the denominator to obtain a decimal number. Multiply the decimal number by 100
Infinite set
Doesn't have a beginning or doesn't have an ending
Equal sets
If set A contains exactly the same elements as set B, A = B. •Both sets are drawn as one circle.
Proper subset
If set A is a proper subset of set B, A ⊂ B. •Circle A is completely inside circle B.
A n C
Is all the elements in set a and c that they have in common
What does it mean to find B n A'
It stand for b intersect a but a is complementary due to the (') therefore you would just list the elements in set B
Union
The union of sets A and B, symbolized A ⋃ B, is the set containing all the elements that are members of set A or of set B (or of both sets). •Regions I, II, and III represents the union.
Universal set
The universal set, symbolized by U, contains all of the elements for any specific discussion.
percent
The word percent comes from the Latin per centum, meaning "per hundred." A percent is a ratio of some number to 100.
Overlapping sets
Two sets A and B with some elements in common. File •This is the most general form of a Venn Diagram.
Disjoint sets
Two sets which have no elements in common are said to be disjoint. •The intersection of disjoint sets is the empty set. •There are no elements in common since there is no overlapping area between the two circles.