[" 10.सिद Do that "a^(*)b=sqrt(a^(2)+b^(2))AA a,b in R" child "],[" Defined "^(*):R times R rarr R" Serials and companions are home. "]

Show that **: RxxR rarr R defined by a^(**) b = a + 2b is not commutative.

The binary operation *:R xx R rarr R is defined as a*b=2a+b* Find (2*3)*4

Show that quad *:R xx R rarr R defined by a*b=a+2b is not commutative.

If * is defined on the set R of all real numbers by a^(*)b=sqrt(a^(2)+b^(2)), find the identity element in R with respect to *

Show that quad *:R xx R rarr R given by (a,b)rarr a+4b^(2) is a binary operation.

f:R rarr R defined by f(x)=(x)/(x^(2)+1),AA x in R is

Show that * : R xx R rarr R defined by a * b =a+2 b is not commutative.

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

Show that *: R xx R to R defined by a*b = 3a + 5b is non commutative and non associative: