Noncommutative

Noncommutative operations

• Division is noncommutative, since ${\displaystyle 1\div 2\neq 2\div 1}$. Subtraction is noncommutative, since ${\displaystyle 0-1\neq 1-0}$. However it is classified more precisely as anti-commutative, since ${\displaystyle x-y=-(y-x)}$ for every ⁠${\displaystyle x}$⁠ and ⁠${\displaystyle y}$⁠. Exponentiation is noncommutative, since ${\displaystyle 2^{3}\neq 3^{2}}$ (see Equation x = y).
• Some truth functions are noncommutative, since their truth tables are different when one changes the order of the operands. For example, the truth tables for (A ⇒ B) = (¬A ∨ B) and (B ⇒ A) = (A ∨ ¬B) are