The binary operation * is defined over the set of real number to be a*b `={:{(asin. (b)/a" if "agtb),(bcos.(a)/b" if " a lt b):}` Find the value of `5**3`

The binary operation defined on the set z of all integers as a ** b = |a-b| - 1 is

The binary operation defined on the set z of all integers as a ** b = |a-b| - 1 is

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

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.

** is a binary operation defined on the set of natural numbers N, defined by a**b = a^b . Find 2**3

** is a binary operation defined on the set of natural numbers N, defined by a**b = a^b . Find 3*2

A binary operation * is defined on the set R of real numbers by a*b={a, if b=0,|a|+b, if b!=0 If atleast one of a and b is 0,then prove that a*b=b*a. Check whether * is commutative.Find the identity element for * ,if it exists

Number of binary operations on the set {a, b} is :