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n mathematics, a matrix (plural matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. Matrices are commonly written in box brackets. The horizontal and vertical lines of entries in a matrix are called rows and columns, respectively. The size of a matrix is defined by the number of rows and columns that it contains. A matrix with m rows and n columns is called an m × n matrix or m m -by- n n n matrix, while m and n are called its dimensions.The dimensions of the following matrix are

2 × 3 2×3

up(read “two by three”), because there are two rows and three columns.

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In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of the matrix A by producing another matrix, often denoted by A T (among other notations).

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In mathematics, particularly in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the number of rows of the first and the number of columns of the second matrix. The product of matrices A and B is denoted as AB.[1][2]Matrix multiplication was first described by the French mathematician Jacques Philippe Marie Binet in 1812,[3] to represent the composition of linear maps that are represented by matrices. Matrix multiplication is thus a basic tool of linear algebra, and as such has numerous applications in many areas of mathematics, as well as in applied mathematics, statistics, physics, economics, and engineering.[4][5] Computing matrix products is a central operation in all computational applications of linear algebra.

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In mathematics, particularly in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the number of rows of the first and the number of columns of the second matrix. The product of matrices A and B is denoted as AB.[1][2]Matrix multiplication was first described by the French mathematician Jacques Philippe Marie Binet in 1812,[3] to represent the composition of linear maps that are represented by matrices. Matrix multiplication is thus a basic tool of linear algebra, and as such has numerous applications in many areas of mathematics, as well as in applied mathematics, statistics, physics, economics, and engineering.[4][5] Computing matrix products is a central operation in all computational applications of linear algebra.

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a mathematical expression that has an equal sign and
linear expressions

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A linear expression is an algebraic expression where each term is either a numeric constant or a variable raised only to the first power. It is most commonly seen in linear equations.

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In mathematics, a system of linear equations (or linear system) is a collection of one or more linear equations involving the same set of variables.] For example,

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In mathematics, a set is a collection of elements.[1][2][3] The elements that make up a set can be any kind of mathematical objects: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.[4] The set with no element is the empty set; a set with a single element is a singleton. A set may have a finite number of elements or be an infinite set. Two sets are equal if and only if they have precisely the same elements.[5]

Sets are ubiquitous in modern mathematics. Indeed, set theory, more specifically Zermelo–Fraenkel set theory, has been the standard way to provide rigorous foundations for all branches of mathematics since the first half of the 20th century.

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Set equality is the term that is used to indicate that two sets are equal. Any two sets, finite or infinite, are equal if they contain the same elements.

Consider two sets, A and B. These two sets are only equal if and only if each element of set A also exists in set B. The order of the two sets’ elements does not matter as long as the elements are the same. Let’s consider the following two sets, A and B, to understand this statement.

A = {1, 2, 3, 4}

B = {2, 4, 1, 3}

By observing the two sets A and B, it is evident that although the two sets A and B are different, they contain the same elements.

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A Venn diagram is a widely used diagram style that shows the logical relation between sets, popularized by John Venn in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple set relationships in probability, logic, statistics, linguistics and computer science. A Venn diagram uses simple closed curves drawn on a plane to represent sets. Very often, these curves are circles or ellipses.

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Mathematical logic is the study of logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power.

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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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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.