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In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. Perhaps most familiar as a property of arithmetic, e.g. "3 + 4 = 4 + 3" or "2 × 5 = 5 × 2", the property can also be used in more ...
In high-level computer programming and digital electronics, logical conjunction is commonly represented by an infix operator, usually as a keyword such as "AND", an algebraic multiplication, or the ampersand symbol &(sometimes doubled as in &&). Many languages also provide short-circuitcontrol structures corresponding to logical conjunction.
Logical disjunction. In logic, disjunction, also known as logical disjunction or logical or or logical addition or inclusive disjunction, is a logical connective typically notated as and read aloud as "or". For instance, the English language sentence "it is sunny or it is warm" can be represented in logic using the disjunctive formula ...
However, many recent programming languages would see an expression like 3 < x < y as consisting of two left (or right-) associative operators, interpreting it as something like (3 < x) < y. If we say that x=4, we then get (3 < 4) < y , and evaluation will give true < y which generally does not make sense.
Elementary algebra. Propositional calculus. In mathematics, the associative property[ 1] is a property of some binary operations that means that rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement for expressions in logical proofs .
A binary operation is a rule for combining the arguments and to produce. In mathematics, a binary operation or dyadic operation is a rule for combining two elements (called operands) to produce another element. More formally, a binary operation is an operation of arity two. More specifically, a binary operation on a set is a binary function ...
A bitwise operation operates on one or more bit patterns or binary numerals at the level of their individual bits.It is a fast, primitive action directly supported by the central processing unit (CPU), and is used to manipulate values for comparisons and calculations.
Binary relation. In mathematics, a binary relation associates elements of one set, called the domain, with elements of another set, called the codomain. [1] Precisely, a binary relation over sets and is a set of ordered pairs consisting of elements from and from . [2]