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2nd year, 1st Sem > COSC 55 > Flashcards

COSC 55 Flashcards

1
Q

it is an unordered collection of objects

A

set

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2
Q

they are the objects contained inside a set

A

elements or members

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3
Q

elements are also called?

A

members

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4
Q

they are used to denote a set

A

uppercase letters

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5
Q

they are used to denote elements

A

lowercase letters

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6
Q

sets can be represented in two ways:

A

roster method
set builder notation

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7
Q

this method is listing down all the elements in a set, only if this is possible

A

roster method

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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

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9
Q

in this method, we specify the rule or property or statement

A

set builder notation

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10
Q

the set is defined by specifying a property that elements of
the set have in common

A

set builder notation

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11
Q

N denotes?

A

natural numbers

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12
Q

Z denotes?

A

integers

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13
Q

R denotes?

A

real numbers

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14
Q

Q denotes?

A

Rational Numbers

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15
Q

C denotes?

A

Complex Numbers

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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

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17
Q

∈ means?

A

belongs to

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18
Q

∉ means?

A

does not belongs to

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19
Q

| or : means?

or : means?

A

such that

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20
Q

∅ means?

A

empty set

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21
Q

|A| means?

A

cardinality

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22
Q

^ means?

A

and

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23
Q

v means?

A

or

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24
Q

it is a set within a set containing the elements of the main
set

A

subset

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25
Q

if two sets contain the same elements they are said to be equal

A

equal set

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26
Q

a set which does not contain any element

A

null/empty/void set

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27
Q

it is a set containing exactly one element

A

singleton set

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28
Q

a set which contains a definite number of element

A

finite set

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29
Q

a set whose elements cannot be listed, i.e., set containing
never ending elements

A

infinite set

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30
Q

it is the number of distinct elements in a given set

A

cardinal number of a set

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31
Q

if two sets do not have any
element in common

A

disjoint set

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32
Q

it is the set of all subsets

A

power set

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33
Q

this set is the combination of all subsets including null set, of a given set

A

power set

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34
Q

a set which contains all the elements of other given sets

A

universal set

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35
Q

what are the two basic set operations are:

A

union of sets
intersection of sets

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36
Q

how to denote a union of the sets A and B?

A

A U B

37
Q

it is the set that contains those elements that are either in A or in B, or in both

A

union of sets

38
Q

how to denote an intersection of sets?

A

A ∩ B

39
Q

it is the set consisting of all elements which are in both sets A and B

A

intersection of sets

40
Q

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

A

product rule

41
Q

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

A

sum rule

42
Q

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

A

subtraction rule

43
Q

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

A

division rule

44
Q

counting problems can be solved by using?

A

tree diagrams

45
Q

it is any linear ordering of the elements of the set, that is, there is a first element, a second, a third, etc.

A

permutation

46
Q

in permutation, n means?

A

number of things

47
Q

in permutation, r means?

A

number to be taken

48
Q

what is the formula in permutation?

A

nPr = n! / (n - r)!

49
Q

it is a set of elements taken regardless of the order in which the elements are arranged

A

combination

50
Q

it consists of simply selecting r elements from a set of n elements without arranging them

A

combination

51
Q

what is the formula in combination?

A

nCr = n! / (n - r)! r!

52
Q

it is the method of expanding a binomial expression which
has been raised to any finite power

A

binomial theorem

53
Q

what is the formula for binomial theorem

A

a + b^n =
n
0
a
n +

n
1
a
n−1b

1 +

n
2
a
n−2b

2 + ⋯ +

n
n
b
n

54
Q

what is the formula for Permutation with Repetition?

A

n^r

55
Q

what is the formula for Combination with Repetition?

A

C(n,r) = (r + n - 1)! / r! (n - 1)

56
Q

what is the formula for Permutation with Indistinguishable Objects?

A

PR^pqr = n! / p! q! r!
n

57
Q

what is the formula for Distinguishable Objects with Distinguishable Boxes?

A

n! / r! r! r! r! natira!

58
Q

what is the formula for Indistinguishable Objects with
Distinguishable Boxes?

A

C(n,r) = (r + n - 1)! / r! (n - 1)

59
Q

it is a measure of the likelihood of a random
phenomenon or chance behavior

A

probability

60
Q

it describes the long-term proportion with which a certain outcome will occur in situations with short-term uncertainty

A

probability

61
Q

Probability means?

A

possibility

62
Q

it is a branch of mathematics that deals with the occurrence of a random event

A

probability

63
Q

probability can be expressed as ?

A

ratio, fraction, decimal, and/or percentage

64
Q

in probability, each repetition of an experiment is a ?

A

trial

65
Q

a possible result of each trial is called

A

outcome

66
Q

it is any process that can be repeated in which the results are uncertain

A

experiment

67
Q

it is any single outcome from a probability experiment

A

simple event

68
Q

each simple event is denoted

A

e

69
Q

it is the likelihood of that event occurring

A

probability of an event

70
Q

probability of an event is denoted as?

A

P(E)

71
Q

the ____ of a probability experiment is the collection of all possible simple events

A

sample space

72
Q

sample space is denoted as?

A

s

73
Q

it is a list of all possible outcomes of a probability experiment

A

sample space

74
Q

it is any collection of outcomes from a probability experiment

A

event

75
Q

events are denoted as?

A

E

76
Q

common terms related to probability

A

experiment
outcomes
equally likely outcomes
sample space
event
sample point

77
Q

a situation involving chance or probability that leads to results called outcomes

A

experiment

78
Q

possible result of a random experiment

A

outcomes

79
Q

all outcomes with equal probability

A

equally likely outcomes

80
Q

set of outcomes in an experiment

A

sample space

81
Q

one or more outcomes in an experiment

A

event

82
Q

each element of the sample space

A

sample point

83
Q

title of lecture 1

A

set and set operations

84
Q

title of lecture 2

A

basic counting principles

85
Q

title of lecture 3

A

permutation and combination

86
Q

title of lecture 4

A

binomial theorem

87
Q

title of lecture 5

A

generalized permutations and combinations

88
Q

title of lecture 6

A

introduction to probability

2nd year, 1st Sem (11 decks)

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