A non-empty set 
together with at least one binary operation defined on it is called an algebraic structure. Thus if G is a non-empty set and “
” is a binary operation on
, then 
is an algebraic structure.
are all algebraic structures. Since addition and multiplication are both binary operations on the set R of real numbers,
is an algebraic structure equipped with two operations.
together with at least one binary operation defined on it is called an algebraic structure. Thus if G is a non-empty set and “” is a binary operation on, then is an algebraic structure.are all algebraic structures. Since addition and multiplication are both binary operations on the set R of real numbers,
is an algebraic structure equipped with two operations.
Example: If the binary operation 
on Q the set of rational numbers is defined by
for every 
show that
is commutative and associative.
Solution:
(1) “
” is commutative in 
because if
, then
on Q the set of rational numbers is defined by for every show that
is commutative and associative.Solution:
(1) “
” is commutative in because if, then
(2) “
” is associative in
because if 
then
” is associative in because if then
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