Learning Disjunction

Definition:

Logical disjunction is an operation on the two logical values, typically the values of two propositions, that produces a value of false if and only if both of its operands are false. More generally a disjunction was a logical formula that can have one or more literals separated only by ORs. A single literal is frequently considered to be a degenerate disjunction.

Properties:

Associativity :

aV (bVc) = (aVb) V c

In mathematics, associativity was a property of some binary operations. It means that, within the expression containing two or more occurrences in a row of the same associative operator, the order in which the operations are performed does not matter as long as the sequence of the operands is not changed. Consider for instance the equation

(5+2) + 1 = 5 + (2+1) = 8

Commutativity:

In mathematics, commutativity is the assets that changing the order of something does not change the end result. It is a primary property of many binary operations, and many mathematical proofs depend on it. The commutativity of easy operations, such as multiplication and addition of numbers, was for many years implicitly assumed and the property was not named until the 19th century when mathematics started to become formalized.

Distributivity:

In mathematics, and in particular to abstract algebra, distributivity is a property of binary operations that generalizes the distributive law from elementary algebra. For example:

2 × (1 + 3) = (2 × 1) + (2 × 3).

Idempotence:

Idempotence is a property of certain operations in mathematics and computer science. Idempotent operations are operations that can apply multiple times without changing the result. The conception of idempotence arises in a number of places in abstract algebra and functional programming.

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Monotonic function:

In mathematics, a monotonic function in which conserve the given order. This concept first arose in calculus, and was shortly generalized to the more abstract setting of order theory.

Symbol:

The mathematical symbol for logical disjunction varies in the text. In addition to the word "or", the symbol "V", deriving from the Latin word vel for "or", is commonly used for disjunction. For example: "A V B " is read as "A or B ". Such a disjunction is false if both A and B are false. In all other cases it is true.

All of the following are disjunctions:

A V B

¬A V B

A V ¬B V ¬C V D V ¬E