Let `@` be an operation defined on `RR`. The set of real numbers, by `a@b=min(a,b)` for all `a,binRR`. Show that `@` is a binary operation on `RR`.

Let ** be an operation defined on NN , the set of natural numbers, by a**b=L.C.M.(a,b) for all a,binNN . Prove that ** is a binary operation on NN .

An operation ** is defined on the set of real numbers RR by a**b=ab+5 for all a,binRR . Is ** a binary operation on RR ?.

let ** be a binary operation on RR , the set of real numbers, defined by a@b=sqrt(a^(2)+b^(2)) for all a,binRR . Prove that the binary operation @ is commutative as well as associative.

Show that an operation ** on RR , the set of real numbers, defined by a**b=3ab+sqrt2, for all a,binRR . Is a binary operaion on RR.

Let *be a binary operation defined on R, the set of all real numbers, by a*b = sqrt(a^(2)+b^(2)), AA a, b in R. Show that is associative on R

Prove that an operation ** on RR , the set of real numbers, defined by x**y=2xy+sqrt5, for all x,yinRR , is a binary operation on RR .

Let * be a binary operation defined on Q, the set of rational numbers, as follows: a*b = a-b, for a , b in Q. Find which of the binary operations are commutative and which are associative.

A binary operation ** is defined on the set of real numbers RR by a**b=2a+b-5 for all a,bin RR . If 3**(x-2)=20 find x.

Let * be a binary operation defined on Q, the set of rational numbers, as follows: a*b =a+ab, for a, b in Q.Find which of the binary operations are commutative and which are associative.

Let ast be a binary operation on the set of real numbers, defined by a astb=frac[ab][5] , for all a,binR . Show that ast is both commutative and associative.