Question

Describe Law of Identity

Answer 1

Law of Identity in Mathematics

An identity in mathematics is a relationship between two mathematical expressions A and B such that A and B generate the same value for all values of the variables within a specified range of validity.

According to the law of identity, if a statement has been determined to be true, it is true.

Boolean Laws

Boolean algebra is the category of algebra in which the variable’s values are the truth values, true and false, ordinary denoted 1 and 0 respectively.

Boolean Algebra Operations

The basic operations of Boolean algebra are as follows:

• Conjunction or AND operation
• Disjunction or OR operation
• Negation or Not operation

Algebraic Identities

The algebraic equations which are valid for all values of variables in them are called algebraic identities.

Standard Algebraic Identities List

All the standard Algebraic Identities are derived from the Binomial Theorem, which is given as:

${(a+b)}^n=C_0^n.a^n.b^0+C_1^n.a^{n-1}.b^1+\dots \dots ..+C_{n-1}^n.a^1.b^{n-1}+C_n^n.a^0.b^n$

Some Standard Algebraic Identities list are given below:

Identity I: ${(a+b)}^2=a^2+2ab+b^2$

Identity II: ${(a–b)}^2=a^2–2ab+b^2$

Identity III: $a^2–b^2=(a+b)(a–b)$

Identity IV:$(x+a)(x+b)=x^2+(a+b)x+ab$

Identity V: ${(a+b+c)}^2=a^2+b^2+c^2+2ab+2bc+2ca$

Identity VI: ${(a+b)}^3=a^3+b^3+3ab(a+b)$

Identity VII: ${(a–b)}^3=a^3–b^3–3ab(a–b)$

Identity VIII: $a^3+b^3+c^3–3abc=(a+b+c)(a^2+b^2+c^2–ab–bc–ca)$

Hence proved.