COSC 55 Flashcards
1
Q
it is an unordered collection of objects
A
set
2
Q
they are the objects contained inside a set
A
elements or members
3
Q
elements are also called?
A
members
4
Q
they are used to denote a set
A
uppercase letters
5
Q
they are used to denote elements
A
lowercase letters
6
Q
sets can be represented in two ways:
A
roster method
set builder notation
7
Q
this method is listing down all the elements in a set, only if this is possible
A
roster method
8
Q
in this method, each element of the set must be listed exactly once. the elements in a set should not be repeated
A
roster method
9
Q
in this method, we specify the rule or property or statement
A
set builder notation
10
Q
the set is defined by specifying a property that elements of
the set have in common
A
set builder notation
11
Q
N denotes?
A
natural numbers
12
Q
Z denotes?
A
integers
13
Q
R denotes?
A
real numbers
14
Q
Q denotes?
A
Rational Numbers
15
Q
C denotes?
A
Complex Numbers
16
Q
what are the different types of sets?
A
subset
equal set
empty/null set
singleton set
finite set
infinite set
cardinal number of a set
disjoint set
power set
universal set
17
Q
∈ means?
A
belongs to
18
Q
∉ means?
A
does not belongs to
19
Q
| or : means?
or : means?
A
such that
20
Q
∅ means?
A
empty set
21
Q
|A| means?
A
cardinality
22
Q
^ means?
A
and
23
Q
v means?
A
or
24
Q
it is a set within a set containing the elements of the main
set
A
subset
25
if two sets contain the same elements they are said to be equal
equal set
26
a set which does not contain any element
null/empty/void set
27
it is a set containing exactly one element
singleton set
28
a set which contains a definite number of element
finite set
29
a set whose elements cannot be listed, i.e., set containing
never ending elements
infinite set
30
it is the number of distinct elements in a given set
cardinal number of a set
31
if two sets do not have any
element in common
disjoint set
32
it is the set of all subsets
power set
33
this set is the combination of all subsets including null set, of a given set
power set
34
a set which contains all the elements of other given sets
universal set
35
what are the two basic set operations are:
union of sets
intersection of sets
36
how to denote a union of the sets A and B?
A U B
37
it is the set that contains those elements that are either in A or in B, or in both
union of sets
38
how to denote an intersection of sets?
A ∩ B
39
it is the set consisting of all elements which are in both sets A and B
intersection of sets
40
this rule says that if there's a procedure can be broken down into a sequence of two tasks, then there are n1*n2 ways to do the procedure
product rule
41
if a task can be done either in one of n1 ways or in one of n2 ways, then there are n1+n2 ways to do the task
sum rule
42
if a task can be done in either n1 ways or n2 ways, then the number of ways to do the task is n1+n2 minus the number of ways to do the tasks that are common to the two different ways
subtraction rule
43
there are n/d ways to do a task if it
can be done using a procedure that can be carried out in n ways, there are d corresponding outcomes per group
division rule
44
counting problems can be solved by using?
tree diagrams
45
it is any linear ordering of the elements of the set, that is, there is a first element, a second, a third, etc.
permutation
46
in permutation, n means?
number of things
47
in permutation, r means?
number to be taken
48
what is the formula in permutation?
nPr = n! / (n - r)!
49
it is a set of elements taken regardless of the order in which the elements are arranged
combination
50
it consists of simply selecting r elements from a set of n elements without arranging them
combination
51
what is the formula in combination?
nCr = n! / (n - r)! r!
52
it is the method of expanding a binomial expression which
has been raised to any finite power
binomial theorem
53
what is the formula for binomial theorem
a + b^n =
n
0
a
n +
n
1
a
n−1b
1 +
n
2
a
n−2b
2 + ⋯ +
n
n
b
n
54
what is the formula for Permutation with Repetition?
n^r
55
what is the formula for Combination with Repetition?
C(n,r) = (r + n - 1)! / r! (n - 1)
56
what is the formula for Permutation with Indistinguishable Objects?
PR^pqr = n! / p! q! r!
n
57
what is the formula for Distinguishable Objects with Distinguishable Boxes?
n! / r! r! r! r! natira!
58
what is the formula for Indistinguishable Objects with
Distinguishable Boxes?
C(n,r) = (r + n - 1)! / r! (n - 1)
59
it is a measure of the likelihood of a random
phenomenon or chance behavior
probability
60
it describes the long-term proportion with which a certain outcome will occur in situations with short-term uncertainty
probability
61
Probability means?
possibility
62
it is a branch of mathematics that deals with the occurrence of a random event
probability
63
probability can be expressed as ?
ratio, fraction, decimal, and/or percentage
64
in probability, each repetition of an experiment is a ?
trial
65
a possible result of each trial is called
outcome
66
it is any process that can be repeated in which the results are uncertain
experiment
67
it is any single outcome from a probability experiment
simple event
68
each simple event is denoted
e
69
it is the likelihood of that event occurring
probability of an event
70
probability of an event is denoted as?
P(E)
71
the ____ of a probability experiment is the collection of all possible simple events
sample space
72
sample space is denoted as?
s
73
it is a list of all possible outcomes of a probability experiment
sample space
74
it is any collection of outcomes from a probability experiment
event
75
events are denoted as?
E
76
common terms related to probability
experiment
outcomes
equally likely outcomes
sample space
event
sample point
77
a situation involving chance or probability that leads to results called outcomes
experiment
78
possible result of a random experiment
outcomes
79
all outcomes with equal probability
equally likely outcomes
80
set of outcomes in an experiment
sample space
81
one or more outcomes in an experiment
event
82
each element of the sample space
sample point
83
title of lecture 1
set and set operations
84
title of lecture 2
basic counting principles
85
title of lecture 3
permutation and combination
86
title of lecture 4
binomial theorem
87
title of lecture 5
generalized permutations and combinations
88
title of lecture 6
introduction to probability
