Algebra Symbols

+

Addition

It combines two or more values.

Solve 5 + 5

solution = 10

-

Subtraction

It finds the difference between the two values.

Solve 10 - 5

solution = 5

* or ×

Multiplication

It multiplies two or more values.

Solve 5 × 2

solution = 10

/ or ÷

Division

Represents sharing or dividing.

Solve 4 ÷ 2

solution = 2

=

Equal to

Indicates correspondence between two expressions.

5 + 5 = 10 Here ,The equal sign denotes that the sum of 5 and 5 is equal to 10

≠

Not equal to

Demonstrates inequality.

5 ≠ 3

The not equal to sign indicates that 5 is not equal to 3

<

Less than

This less than symbol (<) is a principal mathematical symbol used to denote that one amount is smaller than another.

12 < 15

Solution : True, Because 12 is less than of 15

>

Greater than

This Greater than symbol (>) is a principal mathematical symbol used to denote that one amount is Greater than another

15 > 5

Solution : True, Because 15 s greater than of 5

≤

Less than or equal To

This ( ≤ ) symbol represent to less than or equal to. This is used to express that one value is less than or equal to another.

x ≤ 5

Here x is less than or equal to 5

≥

Greater than or Equal To

This ( ≥ ) symbol represents to Greater than or equal To. This is used to express that one value is greater than or equal to another.

x ≥ 6

Here x is greater than or equal to 6

≪

Much less than

Value on left side of the symbol is much less than value on right side

1 ≪ 100

It means 1 is much less than 100

≫

Much greater than

Value on left side of the symbol is much greater than value on right side

1 ≫ 100

it means 1 is much greater than 100

[ ]

Square Brackets

Square brackets, meant by the symbols "[ ]", fill different needs in various contexts, including arithmetic, programming, semantics, and writing conventions

x has a place with the closed interval from 3 to 7, including the both endpoints. This is indicated x as ∈ [3,7].

{ }

Curly Brackets or Set Symbol

Used to group components.

5 × { 4 + 5 }

Here, the curly brackets indicates that the addition operation inside should be perform before multiply with 5

If set A is a set of first 3 natural numbers then A = {1, 2, 3 }

( )

Parentheses

Indicate the request for tasks

(4 + 4) × 3

Here, Parentheses indicates that addition operation should be perform before multiplying.

∧

AND Operation or Conjunction

The AND operation returns True (or 1) provided that both of its operands are True. In emblematic rationale, it is many times addressed by the symbol "∧".

x > 4 ∧ x < 8

This addresses the answer for an inequality where x is greater than 4 and less than 8.

∨

OR Operation or Disjunction

The OR operation returns True (or 1) assuming that something like one of its operands is True. In representative rationale, it is much of the time addressed by the symbol "∨"

x > 5 ∨ x < 6

This addresses the answer for a inequality where x is either less than 2 or greater than 8.

¬

NOT Operation or Negation

The NOT operation returns something opposite to its operand. Assuming the operand is True, NOT returns False (0), and on the off chance that the operand is False, NOT returns True (1). In representative rationale, it is many times addressed by the symbol "¬".

¬ B

In the event that B= {1,2,3}, A( part of B) future the arrangement of all components not in B

{A}

Set A

Set is always denoted by a capital letter in curly bracket

If set A is set of even numbers then

{A} = {2, 4, 6, 8...}

⊂

Subset

Subset means all element of a set is member of another set

Natural Number is subset of integers as all the members of natural numbers are memeber of integers

⊃

Superset

Superset means the set on left side of symbol has all the members of another set

Integeer is superset of Natural Number

⋃

Union of Set

It means combining elements of two sets whiling keeping the common elements only once

A = {2, 3, 4}, B = {2, 4, 6}

Then A ⋃ B = {2, 3, 4, 6}

⋂

Intersection of Set

Intersection of sets means fidning out common elements between two sets

A = {2, 3, 4}, B = {2, 4, 6}

Then A ⋂ B = {2, 4}

n(A)

Cardinality of Set

It denotes the number of elements in a given set

A = {2, 4, 6} then n(A) = 3

Φ

Null Set

Null set means there is no element in that set

Set of Natural Number greater than 2 but less than 3

A_ij

Matrices

Matrix is represented by Capital letters, matrices are arrays of numbers, symbols or expressions

A_{3\times2} = \begin{bmatrix} 1&amp; 2\\ 3&amp; 4\\ 5&amp; 6\\ \end{bmatrix}

| A | or det(A)

Determinant

It represents the Determinant of a square matrix A.

If we have matrix A = \begin{bmatrix} 1&amp; 2\\ 3&amp; 4\\ \end{bmatrix} then

|A| = |1 × 4 - 2 ×3| = 4 - 6 = -2

A^T

Tanspose of Matrix

In Transpose of Matrix, the elements of rows are arranged in column and vice versa

If we have matrix A = \begin{bmatrix} 1&amp; 2\\ 3&amp; 4\\ \end{bmatrix} then

A^T = \begin{bmatrix} 1&amp; 3\\ 2&amp; 4\\ \end{bmatrix}

A^-1

Inverse of Matrix

Inverse of Matrix basically means finding a matrix that when multiplied to orginal matrix give

For Matrix A = \begin{bmatrix} 1&amp; 2\\ 3&amp; 4\\ \end{bmatrix}

A^-1 = \begin{bmatrix} -2&amp; 1\\ 3/2&amp; -1/2\\ \end{bmatrix}

=

Equality

It represents the relation of equality between two values

a = b means that a is equal to b

≠

Inequality

It represents the relation of inequality between two values

a ≠ b that means a is not equal to b

≅

Approximation

It represents that two values are approximately equal

a ≅ b means that a is approximately equal to b

∈

Belongs to

It state that a element belong to a particular set

a ∈ A means that a belongs to set A

∉

Not Belongs to

Element doesn't belong to given set

3 ∉ set of Even Numbers

⋉

Directly Proportional

It means increase in value of one quantity will lead to increase in value of other quantity

Total Bill increases if you buy more product. Hence, total bill is directly proportional to number of objects

→ , ↦

Maps To

It denotes the mapping of an elements to its images under the function

f : X → Y that means function f maps elements from set X to set Y

↔

Bijective Mapping

It indicates one-to-one and onto mapping

f : X ↔ Y that means f that f is a bijective mapping between set X and Y

⇒

Implies

It used in logical statements

X ⇒ Y means if X, then y

⇔

If and Only If

It is basically a biconditional operation

If Corresponding Angles are equal then lines are parallel and if lines are parallel corresponding angles are equal

f(x)

Function

It means Function in terms of x

f(x) = x + 1

Dom(f)

Domain of Function f

It indicate input value of a function

Dom (Sin x) = R

Range (f)

Range of Function f

It indicate Range of Function f

Range (Sin x) = [1, 1]

fog

Composition of Function

It means function f is described in terms of function g

If f = sin x and g = x + 2

Then fog = sin(x + 2)

⌊x⌋

Fllor of x

It indicates the greatest integer less than x

⌊4.46⌋ = 4

⌈x⌉

Ceiling of x

It indicates the smallest integer greater than x

⌈4.46⌉ = 5

\vec V

Vector V

V is a quantity that has both magnitude and direction

\vec V = x\hat i + y\hat j + z\hat k

|\vec V|

Magnitude of Vector V

It indicates the scalar length of vector V

For a vector V = (2i + 3j + k), it magnitude is √(2² + 3² + 1²) = 3.74

u + v

Vector Addition

(u₁ + v₁, u₂ + v₂, u₃ + v₃)

Consider two vectors u = ( 2 , 3, 1) and v = ( 1, 2, 3)

u + v = ( 2,3,1) + (1,2,3) = (3, 5, 4)

c . u

Scalar Multiplication

( c . u₁ , c . u₂, c. u₃)

c = 3 , u = (3, 2, 1)

3 . u = 3 . ( 3,2,1) =

(9, 6,3)

u . v

Dot Product

uv cos θ

u.v = (i + 2j + 3k).(3i + 4j + 5k) = 26

u ⨯ v

Cross Product

uv Sin θ

u ⨯ v = (3i + 4j + 5 k) ⨯ (i + 2j + 3k) = 2i -j + 2k

=

Equal

!=

Not Equal

+

Addition

-

Subtraction

/

Division

*

Multiplication

>

Greater Than

<

Less Than

( )

Parentheses

{ }

Curly Braces

[ ]

Square Braces

|X|

Modulus

П

Pi(3.14159)

^

Exponentiation

≥

Greater than or Equal to

≤

Less than or Equal to

∝

Proportional To

∷

Equal Proportional To

⋉

Direct Proportional To

f( x )

Represent Function Name

f ^-1

Represent Inverse Function Name