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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.

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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

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Matrix Product (or Matrix Multiplication)

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Matrix Product (or Matrix Multiplication)

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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.

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A mathematical expression that has an equal sign andlinear expressions

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A mathematical statement that performs functions of addition, subtraction, multiplication, and division

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Equations that can be written in the form where a and b are real numbers, with are linear equations. Examples

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A “system” of equations is a set of equations that are related to
one another (have common variables).

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For example, the red point is not a solution to the system, because it
is not on either line.

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•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.

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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.”

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•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

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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

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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.

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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}

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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}

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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.

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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

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Let p and q be propositions. The conjunction of p and q,
denoted by p Ù q, is the proposition “p and q.”

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Let p and q be propositions. The disjunction of p and q, denoted
by p v q, is the proposition “p or q.”

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Conditional Proposition or a Material Implication

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Conditional Proposition or a Material Implication

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•Inverter, Or, And, XOR gate symbols, etc.
•Multi-input gates.
•Logic circuits and examples.
•Adders, “half,” “full,” and n-bit.

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•Inverter (logical NOT, Boolean complement).
•AND gate (Boolean
product).
•OR gate (Boolean sum).
•XOR gate (exclusive-OR sum mod 2).

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The linear equations are easily understandable.

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The linear equations are easily understandable.

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I still don't quite understand the mark in this lesson

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Still a little confused but I can understand it better later