COSC 55 Flashcards
it is an unordered collection of objects
set
they are the objects contained inside a set
elements or members
elements are also called?
members
they are used to denote a set
uppercase letters
they are used to denote elements
lowercase letters
sets can be represented in two ways:
roster method
set builder notation
this method is listing down all the elements in a set, only if this is possible
roster method
in this method, each element of the set must be listed exactly once. the elements in a set should not be repeated
roster method
in this method, we specify the rule or property or statement
set builder notation
the set is defined by specifying a property that elements of
the set have in common
set builder notation
N denotes?
natural numbers
Z denotes?
integers
R denotes?
real numbers
Q denotes?
Rational Numbers
C denotes?
Complex Numbers
what are the different types of sets?
subset
equal set
empty/null set
singleton set
finite set
infinite set
cardinal number of a set
disjoint set
power set
universal set
∈ means?
belongs to
∉ means?
does not belongs to
| or : means?
or : means?
such that
∅ means?
empty set
|A| means?
cardinality
^ means?
and
v means?
or
it is a set within a set containing the elements of the main
set
subset
if two sets contain the same elements they are said to be equal
equal set
a set which does not contain any element
null/empty/void set
it is a set containing exactly one element
singleton set
a set which contains a definite number of element
finite set
a set whose elements cannot be listed, i.e., set containing
never ending elements
infinite set
it is the number of distinct elements in a given set
cardinal number of a set
if two sets do not have any
element in common
disjoint set
it is the set of all subsets
power set
this set is the combination of all subsets including null set, of a given set
power set
a set which contains all the elements of other given sets
universal set
what are the two basic set operations are:
union of sets
intersection of sets
how to denote a union of the sets A and B?
A U B
it is the set that contains those elements that are either in A or in B, or in both
union of sets
how to denote an intersection of sets?
A ∩ B
it is the set consisting of all elements which are in both sets A and B
intersection of sets
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
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
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
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
counting problems can be solved by using?
tree diagrams
it is any linear ordering of the elements of the set, that is, there is a first element, a second, a third, etc.
permutation
in permutation, n means?
number of things
in permutation, r means?
number to be taken
what is the formula in permutation?
nPr = n! / (n - r)!
it is a set of elements taken regardless of the order in which the elements are arranged
combination
it consists of simply selecting r elements from a set of n elements without arranging them
combination
what is the formula in combination?
nCr = n! / (n - r)! r!
it is the method of expanding a binomial expression which
has been raised to any finite power
binomial theorem
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
what is the formula for Permutation with Repetition?
n^r
what is the formula for Combination with Repetition?
C(n,r) = (r + n - 1)! / r! (n - 1)
what is the formula for Permutation with Indistinguishable Objects?
PR^pqr = n! / p! q! r!
n
what is the formula for Distinguishable Objects with Distinguishable Boxes?
n! / r! r! r! r! natira!
what is the formula for Indistinguishable Objects with
Distinguishable Boxes?
C(n,r) = (r + n - 1)! / r! (n - 1)
it is a measure of the likelihood of a random
phenomenon or chance behavior
probability
it describes the long-term proportion with which a certain outcome will occur in situations with short-term uncertainty
probability
Probability means?
possibility
it is a branch of mathematics that deals with the occurrence of a random event
probability
probability can be expressed as ?
ratio, fraction, decimal, and/or percentage
in probability, each repetition of an experiment is a ?
trial
a possible result of each trial is called
outcome
it is any process that can be repeated in which the results are uncertain
experiment
it is any single outcome from a probability experiment
simple event
each simple event is denoted
e
it is the likelihood of that event occurring
probability of an event
probability of an event is denoted as?
P(E)
the ____ of a probability experiment is the collection of all possible simple events
sample space
sample space is denoted as?
s
it is a list of all possible outcomes of a probability experiment
sample space
it is any collection of outcomes from a probability experiment
event
events are denoted as?
E
common terms related to probability
experiment
outcomes
equally likely outcomes
sample space
event
sample point
a situation involving chance or probability that leads to results called outcomes
experiment
possible result of a random experiment
outcomes
all outcomes with equal probability
equally likely outcomes
set of outcomes in an experiment
sample space
one or more outcomes in an experiment
event
each element of the sample space
sample point
title of lecture 1
set and set operations
title of lecture 2
basic counting principles
title of lecture 3
permutation and combination
title of lecture 4
binomial theorem
title of lecture 5
generalized permutations and combinations
title of lecture 6
introduction to probability
