According to the law of identity, if a statement has been determined to be true, it is true.
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.
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
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 = nC0.an.b0+ nC1.an−1.b1+……..+ nCn−1.a1.bn−1+ nCn.a0.bn
Some Standard Algebraic Identities list are given below:
Identity I: (a + b)2 = a2 + 2ab + b2
Identity II: (a – b)2 = a2 – 2ab + b2
Identity III: a2 – b2= (a + b)(a – b)
Identity IV: (x + a)(x + b) = x2 + (a + b) x + ab
Identity V: (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
Identity VI: (a + b)3 = a3 + b3 + 3ab (a + b)
Identity VII: (a – b)3 = a3 – b3 – 3ab (a – b)
Identity VIII: a3 + b3 + c3 – 3abc = (a + b + c)(a2 + b2 + c2 – ab – bc – ca)