https://padlet.com/6331306019/159dcw9w3gbr0ei4 Mathematics for Information Technology 2 en-us 2021-09-12 12:05:56 UTC 2025-11-04 22:45:20 UTC hello@padlet.com 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733584398 A matrix is a rectangular array of numbers. A matrix with m rows and n columns is called an m × n matrix. The plural of matrix is matrices. A matrix with the same number of rows as columns is called square. Two matrices are equal if they have the same number of rows and the same number of columns and the corresponding entries in every position are equal.]]> 2021-09-12 12:11:55 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733584398 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733586009 2021-09-12 12:13:47 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733586009 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733586802 2021-09-12 12:14:39 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733586802 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733589478 The sum of two matrices of the same size is obtained by adding elements in the corresponding positions. Matrices of different sizes cannot be added, because the ]]> 2021-09-12 12:17:25 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733589478 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733592947 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 12:21:13 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733592947 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733600495 2021-09-12 12:28:50 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733600495 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733601570 2021-09-12 12:29:54 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733601570 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733602323 A mathematical expression that has an equal sign andlinear expressions]]> 2021-09-12 12:30:45 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733602323 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733603221 A mathematical statement that performs functions of addition, subtraction, multiplication, and division]]> 2021-09-12 12:31:35 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733603221 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733604114 Equations that can be written in the form where a and b are real numbers, with are linear equations. Examples]]> 2021-09-12 12:32:31 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733604114 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733605075 A “system” of equations is a set of equations that are related to
one another (have common variables).]]> 2021-09-12 12:33:35 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733605075 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733605969 For example, the red point is not a solution to the system, because it
is not on either line.]]> 2021-09-12 12:34:33 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733605969 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733607630 2021-09-12 12:36:13 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733607630 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733609889 2021-09-12 12:38:15 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733609889 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733611367 •A set is a collection of objects, things or symbols which are clearly defined.
•The individual objects in a set are called the members or elements of the set.
•A set must be properly defined so that we can find out whether an object is a member of the set.]]> 2021-09-12 12:39:38 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733611367 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733612221 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 12:40:25 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733612221 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733614397 •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 12:42:30 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733614397 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733615597 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 12:43:35 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733615597 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733618941 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 12:46:20 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733618941 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733624205 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 12:50:35 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733624205 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733625975 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 12:52:07 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733625975 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733628433 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 12:54:15 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733628433 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733629820 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 12:55:29 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733629820 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733631004 2021-09-12 12:56:31 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733631004 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733632349 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 12:57:37 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733632349 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733633130 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 12:58:14 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733633130 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733634559 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 12:59:24 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733634559 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733636293 2021-09-12 13:00:39 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733636293 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733636883 •Inverter, Or, And, XOR gate symbols, etc.
•Multi-input gates.
•Logic circuits and examples.
•Adders, “half,” “full,” and n-bit.]]> 2021-09-12 13:01:07 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733636883 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733638108 •Inverter (logical NOT, Boolean complement).
•AND gate (Boolean
product). 
•OR gate (Boolean sum). 
•XOR gate (exclusive-OR sum mod 2).]]> 2021-09-12 13:02:00 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733638108 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733639588 2021-09-12 13:03:04 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733639588 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733641664 2021-09-12 13:04:38 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733641664 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733646166 2021-09-12 13:08:04 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733646166 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733647568 2021-09-12 13:09:09 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733647568 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733651454 2021-09-12 13:12:13 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733651454 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733657537 I still don't quite understand the mark in this lesson]]> 2021-09-12 13:16:43 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733657537 6331306019 https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733662444 Still a little confused but I can understand it better later]]> 2021-09-12 13:20:22 UTC https://padlet.com/6331306019/159dcw9w3gbr0ei4/wish/1733662444