Identity Law In Boolean Algebra
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FAQ
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 "identity" is merely a relationship that is always true, regardless of the values that any variables involved might take on; similar to laws or properties. Many of these can be analogous to normal multiplication and addition, particularly when the symbols {0,1} are used for {FALSE, TRUE}.
Laws and Theorems of Boolean Algebra 4a.X ? X = 0Complement Law5.X = XDouble Negation Law6a.X ? Y = Y ? XCommutative Law7a.X (Y Z) = (X Y) Z = (X Z) Y = X Y ZAssociative Law7b.X + (Y + Z) = (X + Y) + Z = (X + Z) + Y = X + Y + ZAssociative Law14 more rows
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.
