https://padlet.com/6331306064/kjspsdbbextno3ac Mathematics for Information Technology 2 en-us 2021-09-12 06:46:34 UTC 2023-03-02 15:47:26 UTC hello@padlet.com 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733464692 2021-09-12 09:51:17 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733464692 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733466559 2021-09-12 09:52:48 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733466559 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733467500 2021-09-12 09:53:31 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733467500 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733468024 2021-09-12 09:54:06 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733468024 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733468906 The sum of two matrices of the same size is obtained by adding elements in the correspondingpositions. Matrices of different sizes cannot be added, because the sum of two matrices is definedonly when both matrices have the same number of rows and the same number of columns.    ]]> 2021-09-12 09:55:03 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733468906 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733469333 In Figure 1 the colored row of A and the colored column of B are used to compute the element
cij of AB. The product of two matrices is not defined when the number of columns in the first
matrix and the number of rows in the second matrix are not the same.]]> 2021-09-12 09:55:32 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733469333 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733471745 2021-09-12 09:58:15 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733471745 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733472108 2021-09-12 09:58:40 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733472108 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733473367 A mathematical expression that has an equal sign andlinear expressions]]> 2021-09-12 09:59:57 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733473367 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733473593 A mathematical statement that performs functions ofaddition, subtraction, multiplication, and division]]> 2021-09-12 10:00:09 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733473593 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733474606 Equations that can be written in the form where a and b are real numbers, with are linear equations. Examples]]> 2021-09-12 10:01:12 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733474606 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733475265 A “system” of equations is a set of equations that are related to
one another (have common variables).]]> 2021-09-12 10:01:51 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733475265 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733475856 For example, the red point is not a solution to the system, because it
is not on either line.]]> 2021-09-12 10:02:32 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733475856 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733477619 2021-09-12 10:04:21 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733477619 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733478027 2021-09-12 10:04:43 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733478027 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733479321 •A set is a collection of objects, things or symbolswhich are clearly defined.
•The individual objects in a set are called themembers or elements of the set.
•A set must be properly defined so that we canfind out whether an object is a member of theset.]]> 2021-09-12 10:06:08 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733479321 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733479757 1. Listing the elements
The set can be defined by listing all its
elements, separated by commas and enclosed
within braces.

Example:
B = {2, 4, 6, 8, 10}
X = {a, b, c, d, e}

2. Describing the elements
The set can be defined, where possible, by
describing the elements.

Example:
C = {x : x is an integer, x > – 3 }
This is read as: “C is the set of elements x such
that x is an integer greater than –3.”]]> 2021-09-12 10:06:35 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733479757 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733481015 •We relate a member and a set using the symbol ∈.
§If an object x is an element of set A, we write x ∈ A. If
an object z is not an element of set A, we write z ∉ A.
•∈ denotes “is an element of” or “is a member of” or
“belongs to”
•∉ denotes “is not an element of” or “is not a member
of” or “does not belong to”

•Example:
If A = {1, 3, 5} then 1 ∈ A and 2 ∉ A]]> 2021-09-12 10:07:55 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733481015 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733481928 An infinite set is a set which is not finite. It is not
possible to explicitly list out all the elements of an
infinite set.
Example:

T = {x : x is a triangle}
N is the set of natural numbers
A is the set of fractions]]> 2021-09-12 10:08:51 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733481928 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733483726 If every element of a set B is also a member of a set A,
then we say “B is a subset of A”.
We use the symbol ⊂ to mean “is a subset of” and ⊄ to
mean “is not a subset of”

Example:
A = {1, 3, 5}, B = {1, 2, 3, 4, 5}
So, A ⊂ B because every element in A is also in B.
X = {1, 3, 5}, Y = {2, 3, 4, 5, 6}.
X ⊄ Y because 1 is in X but not in Y.]]> 2021-09-12 10:10:49 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733483726 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733484752 A universal set is the set of all elements under consideration,
denoted by capital U or sometimes capital E.

Example: Given that U = {5, 6, 7, 8, 9, 10, 11, 12}, list the
elements of the following sets.
a) A = {x : x is a factor of 60}
b) B = {x : x is a prime number}
Solution: The elements of sets A and B can only be selected
from the given universal set U .
a) A = {5, 6, 10, 12}
b) B = {5, 7, 11}]]> 2021-09-12 10:11:51 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733484752 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733486322 The intersection of two sets X and Y is the set of
elements that are common to both set X and set
Y. It is denoted by X ∩ Y and is read ‘X
intersection Y’.

Example:
Draw a Venn diagram to represent the
relationship between the sets
X = {1, 2, 5, 6, 7, 9}, Y = {1, 3, 4, 5, 6, 8} 
and Z = {3, 5, 6, 7, 8, 10}
Solution: We find that X ∩ Y ∩ Z = {5, 6}, 
X ∩ Y = {1, 5, 6}, Y ∩ Z = {3, 5, 6, 8} and X ∩ Z = {5, 6, 7}]]> 2021-09-12 10:13:26 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733486322 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733488223 Definition
A proposition (p, q, r, ...) is simply a statement (i.e., a
declarative sentence) with a definite meaning, having a truth
value that’s either true (T) or false (F) (never both, neither,
or somewhere in between).

Example
• p: Today is Sunday.
• q: 1+1=9-8.
• r: Bangkok is the capital of Thailand.
• t: I got “A” in Math for IT II.]]> 2021-09-12 10:15:19 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733488223 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733489143 Example: Not Proposition
• p: Let’s drink.
• q: a+b.
• r: Take a rest.
• S: A-B=3.
• t: DO IT NOW!
• u: The School of IT]]> 2021-09-12 10:16:18 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733489143 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733491138 2021-09-12 10:18:19 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733491138 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733491436 Let p and q be propositions. The conjunction of p and q,
denoted by p Ù q, is the proposition “p and q.”]]> 2021-09-12 10:18:39 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733491436 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733491638 Let p and q be propositions. The disjunction of p and q, denoted
by p v q, is the proposition “p or q.”]]> 2021-09-12 10:18:55 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733491638 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733494181 It looks like something has changed since you first loaded this page. Reloading the page often fixes the problem. Please reload page to continue contributing.]]> 2021-09-12 10:21:44 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733494181 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733494999 2021-09-12 10:22:39 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733494999 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733495304 •Inverter, Or, And, XOR gate symbols, etc.
•Multi-input gates.
•Logic circuits and examples.
•Adders, “half,” “full,” and n-bit.]]> 2021-09-12 10:22:56 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733495304 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733495957 •Inverter (logical NOT, Boolean complement).
•AND gate (Boolean
product). 
•OR gate (Boolean sum). 
•XOR gate (exclusive-OR sum mod 2).]]> 2021-09-12 10:23:39 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733495957 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733498279 2021-09-12 10:25:41 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733498279 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733498373 2021-09-12 10:25:48 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733498373 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733498485 2021-09-12 10:25:54 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733498485 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733502092 2021-09-12 10:29:56 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733502092 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733502133 2021-09-12 10:29:59 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733502133 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733502567 I still don't quite understand ]]> 2021-09-12 10:30:31 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733502567 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733503116 Still a little confused ]]> 2021-09-12 10:31:11 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1733503116 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1807770796 Probability: what is the chance that a given event will occur
} Probability is expressed in numbers between 0 and 1.
◦ Probability = 0 means the event never happens.
◦ Probability = 1 means it always happens.
} The total probability of all possible events always sums to 1.
} The probability of an event equals the number of times it
happens divided by the number of total opportunities.
} These numbers can be determined by experiment or by
knowledge of the system.]]> 2021-10-11 14:10:51 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1807770796 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1807772775 ◦ The probability of 2 independent events both happening is the product of their individual probabilities.

◦ Called the AND rule because “this event happens AND that event
happens”.

◦ Example: What is the probability of rolling a 2 on one die and a 2 on
a second die?

Solution: For each event, the probability is 1/6,
So the probability of both happening is 1/6 x 1/6 = 1/36.]]> 2021-10-11 14:11:29 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1807772775 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1807773968 ◦ The probability that either one of 2 different events will occur is the sum
of their separate probabilities.

Example: The chance of rolling either a 2 or a 3 on a die is :

1/6 + 1/6 = 1/3.]]> 2021-10-11 14:11:52 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1807773968 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1807774716 ◦ The chance of an event not happening is 1 minus the chance of it
happening.

◦ Example: The chance of not getting a 2 on a die is :

1 - 1/6 = 5/6.

◦ This rule can be very useful. Sometimes complicated problems are
greatly simplified by examining them backwards.]]> 2021-10-11 14:12:06 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1807774716 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1807776191 ◦ More complicated situations involve combining the AND and OR rules.
◦ It is very important to keep track of the individuals involved and not
allow them to be confused. This is the source of most people’s
problems with probability.
◦ Example: What is the chance of rolling 2 dice and getting a 2 and a 5?

The trick is, there are 2 ways to accomplish this: a 2 on die A

and a 5 on die B, or a 5 on die A and a 2 on die B.

Each possibility has a 1/36 chance of occurring, and you want

either one or the other of the 2 events,

So the final probability is 1/36 + 1/36 = 2/36 = 1/18.]]> 2021-10-11 14:12:31 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1807776191 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1807779838  Knowing that an event B occurred might affect the probability that
another event A also occurred

 Reduce the effective sample space from S to B, then measure “size” of
A relative to its overlap (if any) in B, rather than relative to S
 If A and B are two events, the probability of event A when we already
know that event B has occurred is]]> 2021-10-11 14:13:41 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1807779838 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1807781038 2021-10-11 14:14:05 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1807781038 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1807783263 An experiment in which a single action, such as flipping a coin,
is repeated identically over and over. The possible results of
the action are classified as "success" or "failure“ ( only two
possible outcomes).
The binomial probability formula is used to find probabilities
for Bernoulli trials.]]> 2021-10-11 14:14:46 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1807783263 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1807786157 2021-10-11 14:15:41 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1807786157 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1807789040 2021-10-11 14:16:35 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1807789040 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1807879787 • Refers to the value of opportunity (Chance) or Possibility (Possibility).
which can be measured in numbers ( 0 to 1 )
• Used in conjunction with many business decision theories such as
• Expected Return
• Investment risk value or return risk value.
from investment (Risk)
• Queuing Theory
• etc. ]]> 2021-10-11 14:44:01 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1807879787 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1807891992 • n(E) = Method number of things or events. only we are interested in
• n(S) = The total number of possible methods associated with an object or event.
What we're interested in is called Numbers of Samples space.
• P(E) or P = probability of event E. ]]> 2021-10-11 14:47:49 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1807891992 6331306064 https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1807892897 2021-10-11 14:48:06 UTC https://padlet.com/6331306064/kjspsdbbextno3ac/wish/1807892897