Algebra Symbols

Algebra Symbols are specific characters that are used to represent particular operations in Algebra. The branch of Algebra deals with the relation between variables and constants. There are different branches of Algebra such as linear algebra, vector algebra, and boolean algebra for which we have different algebra symbols.

In this article, we will learn how to represent variables and constants in algebra and also different symbols

What is Algebra?

Algebra is a branch of mathematics that deals with the relation between variables and constants and finding the value of variables and any such unknown quantities. Algebra uses statements that consist of variables and constants to represent any mathematical or physical problem and find its solution using different operations. Such expressions that consist of variables and constants are called Algebraic Expression. Example 2a+b where a and b are variables and 2 is constant.

When these algebraic expressions are equated to some other variable or constant these algebraic expressions are called equations. Example, 2a + b = 3b. Algebra is also further subdivided into various other branches that use symbols that have specific meanings. Let’s learn these symbol names, along with their meaning and examples.

Learn More,

• Algebra
• Algebraic Expression

Algebra Symbols in Maths

Algebra symbols in maths are the unique characters that have their specific meaning in a mathematical operation. Any algebraic expression mainly consists of variables and constants. Let’s learn first what is the symbol of variable and constant.

Variable Symbol

Variable as the name suggests has no fixed value and their value change in different situations. Variables in Algebra are represented by Alphabets such as A, B, C… or a, b, c…. and by Greek Letters such as α, β, γ, etc. The unknown angle is represented by θ

Constant Symbol

Constant are those which have fixed value. Constant in algebra are represented by Numbers in maths such as 1, 2, 3, -1, -2…. Greek letters such as pi(π) is also a constant whose value is approximately equal to 3.14, and euler’s number ‘e’ whose value is equal to 2.71

Let’s learn all the algebra symbols used in different sub-branches of algebra

Fundamental Operators

The symbol of various fundamental operators in algebra is tabulated below:

SYMBOL	NAME	MEANING/DEFINITION	EXAMPLE
+	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

Inequalities Symbols

The inequalities symbols used in Algebra are tabulated below:

SYMBOL	NAME	MEANING/ DEFINITION	EXAMPLE
=	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

Learn Inequality Concepts

• Inequalities
• Linear Inequality

Grouping Symbols

Constant and Variables in algebra can be grouped together when a common factor is taken out of them. The grouping symbols in algebra is tabulated below:

SYMBOL	NAME	MEANING/ DEFINITION	EXAMPLE
[ ]	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.

Boolean Algebra Symbols

Boolean Algebra is a branch of akgebra that uses logical operations such as conjusction, disjunction and negation and give the value in True or False. The symbols for the operations in Boolean Algebra is tabulated below:

SYMBOL	NAME	MEANING/ DEFINITION	EXAMPLE
∧	AND Operation or Conjuction	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

Linear Algebra Symbols

Linear Algebra includes the study of matrices, set theory, determinant etc. The symbol used in Linear Algebra are used

SYMBOL	NAME	MEANING/DEFINITION	EXAMPLE
{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
Aij	Matrices	Matrix is represented by Capital letters, matrices are arrays of numbers, symbols or expressions
| A | or det(A)	Determinant	It represents the Determinant of a square matrix A.	If we have matrix A = then |A| = |1 × 4 – 2 ×3| = 4 – 6 = -2
AT	Tanspose of Matrix	In Transpose of Matrix, the elements of rows are arranged in column and vice versa	If we have matrix A = then AT =
A-1	Inverse of Matrix	Inverse of Matrix basically means finding a matrix that when multiplied to orginal matrix give	For Matrix A = A-1 =

Read Linear Algebra Concepts

• Set Theory
• Matrices
• Determinant

Relation Symbols

The Relation symbol deals with the approximation, directly proportional etc. The relation symbols are tabulated below:

SYMBOL	NAME	MEANING/DEFINITION	EXAMPLE
=	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

Function Symbols

The general symbols used in functions are tabulated below:

SYMBOL	NAME	MEANING/DEFINITION	EXAMPLE
→ , ↦	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

Read Function Concepts

• Function
• Types of Function
• Domain and Range of Function

Vector Algebra

The symbols used in Vector Algebra are tabulated below:

SYMBOL	NAME	MEANING/DEFINITION	EXAMPLE
	Vector V	V is a quantity that has both magnitude and direction
	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

Read Vector Concepts

• Dot and Cross Product
• Magnitude of Vector

Table of Algebra Symbols

The table of common of algebra symbols are tabulated below:

SYMBOL	NAME
=	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

Solved Examples on Algebra Symbols

Example 1: Given two vales A = 5 and B = 10, Find the value of A and B By using Addition

Solution:

A + B = 5 + 10 = 15

Example 2: For the equation 2x – 3 = 2, Solve for x

Solution:

2x – 3 = 2

⇒ 2x = 2 + 3

⇒ 2x = 5

⇒ x = 5 / 2

⇒ x = 2.5

Example 3: Solve the quadratic expression x² + 5x + 5

Solution:

x² + 5x + 6

= x² + 2x + 3x + 6

= ( x + 2 ) ( x + 3)

Example 4: Given two values A = 10 and B = 20, Find the product of A and B

Solution:

Product of A and B = A × B = 10 × 20 = 200

Example 5: Given two values A = 20 and B = 5, Find the quotient of A and B by using Division

Solution:

Quotient of A and B = A/B = 20/5 = 4

Example 6: Find either True or False 12 < 15. Give reason while it was True

Solution:

True, Because 12 is less than of 15

Practice Examples on Algebra Symbols

Q1. Find the sum of 35 and 60

Q2. Find the Difference of 67 and 39

Q3. Simplify the expression: 5x + 2(8 – 4x)

Q4. Solve the equation for x: 8( x – 4 ) = 2x + 6

Q5. Solve Quadratic Equation for x in the equation 2x² – 5x + 3 = 0

Algebra Symbols – FAQs

1. What is an Algebra Symbol?

A algebra symbol is a character or notation utilized in algebraic expression or conditions to address numerical tasks, connections, or quantities.

2. What is the meaning of the equivalent sign (=) in algebra?

The equivalent sign (=) is an essential polynomial algebra symbol addressing equality. It demonstrates that the articulations on the two sides of the sign have a similar worth. Tackling conditions includes controlling images to find the upsides of factors that fulfill the equality.

3. How are Algebra Symbols used in Equations?

Algebra symbol are utilized to establish relation between constant and variables in maths. For example, in the equation 5x +2 = 6

4. What does |x| represent in Algebra?

|x| represent absolute value of x. It is also called modulus of x

5. How Represent a Function in Algebra?

In Algebra Function is represented by f(x)

6. What does A ⋉ B signify?

A ⋉ B signifies that A is directly proportional to B. It means if B becomes twice of itself, A will also become twice of itself