Question

What is the law of identity?

Answer 1

Hint: First, we will describe the law of identity and then we will state the types of identity we use in mathematics. Since there are so many identities, hence we will only mention some of them. Finally, we will give some examples to make the concept clearer.

Complete step-by-step solution:
According to the law of identity, it is true if a statement is determined to be true, the law of identity states that all things are identical to themselves. Identity law can be stated as A=A. An identity is an equivalence between differently defined functions. In other words, A = B is identity when A and B define the same functions. The concept of identity is essential because it explicitly explains that reality is definite since there cannot be two identities for an entity. It states that every object that exists consists of its own special features, which are part of what it is. In mathematics, we use various types of identities and some of them are listed below.
A) Algebraic Identities
B) Trigonometric Identities
C) Exponential Identities
D) Logarithmic Identities
Some of the examples of identities provided above are-
1) \[{(a + b)^2} = {a^2} + {b^2} + 2ab \Rightarrow \] Algebraic Identities
2) \[{\cos ^2}\theta + {\sin ^2}\theta = 1 \Rightarrow \] Trigonometric Identities
3) \[{x^{m + n}} = {x^m} \times {x^n} \Rightarrow \] Exponential Identities
4) \[\log (xy) = \log x + \log y \Rightarrow \] Logarithmic Identities

Note: The Law of Identity is one of the Boolean Laws; it includes two terms:
1 AND A = A means a product of 1 and any number or variable is the same number and variable and 0 OR A = A means a sum of 0 and any number or variable is the same number or variable.