associative law meaning in Hindi

Examples

1. There the associative law is replaced by the Jacobi identity.
2. The Cayley plane uses octonion coordinates which do not satisfy the associative law.
3. This operation on rotations obeys the associative law, but can fail the commutative law.
4. If the product operation is associative, the generalized associative law says that all these formulas will yield the same result, making the parenthesis unnecessary.
5. A partial groupoid ( M, \ circ ) is called a "'partial semigroup "'if the following associative law holds:
6. The associative laws of addition and multiplication allow adding terms in any order, and multiplying factors in any order but mixed operations must obey the standard order of operations.
7. Leonhard Euler considered algebraic operations on numbers modulo an integer, modular arithmetic, in associative law for the composition of forms, but like Euler before him, he seems to have been more interested in concrete results than in general theory.
8. While some of the familiar rules of arithmetic algebra continue to hold in the algebra of propositions ( e . g . the commutative and associative laws for AND and OR ), some do not ( e . g . the distributive laws for AND, OR and NOT ).
9. But this is nothing more than the geometric version of the ( left ) distributive law, a ( b + c + d ) = ab + ac + ad; and in Books V and VII of the " Elements " the commutative and associative laws for multiplication are demonstrated.
10. In 1932, Jordan attempted to axiomatize quantum theory by saying that the algebra of observables of any quantum system should be a formally real algebra which is commutative ( " xy " = " yx " ) and power-associative ( the associative law holds for products involving only " x ", so that powers of any element " x " are unambiguously defined ).