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So the identity law, p?T?p, means that the conjunction of any sentence p with an arbitrary tautology T will always have the same truth value as p (i.e., will be logically equivalent with p).
An algebraic identity is an equality that holds for any values of its variables. For example, the identity ( x + y ) 2 = x 2 + 2 x y + y 2 (x+y)^2 = x^2 + 2xy + y^2 (x+y)2=x2+2xy+y2 holds for all values of x and y.
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.
In logic, the law of identity states that each thing is identical with itself. It is the first of the historical three laws of thought, along with the law of noncontradiction, and the law of excluded middle.
The Identity Law is one of the Boolean Laws; it has two expressions: 1 AND A = A - the product of 1 and any number or variable is the number or variable itself. And. 0 OR A = A - the sum of 0 and any number or variable is the number or variable itself.