Prove that 0 is the identity element of the binary operation `**` on `ZZ^(+)` defined by `x**y=x+y` for all `x,yinZZ^(+)`.

Find the identity element of the binary operation ** on ZZ defined by a**b=a+b+1 for all a,binZZ .

Prove that the identity element of the binary opeartion ** on RR defined by a**b = min. (a,b) for all a,binRR , does not exist.

Define identity element for a binary operation defined on a set.

Define identity element for a binary operation defined on a set.

The identity element for the binary operation * defined on Q - (0) as a * b = (ab)/(2) for all a , b in Q - (0) is

A binary operation ** is defined on the set S={0,1,2,3,4} as follows: a**b=a+b(mod5) Prove that 0inS is the identity element of the binary operation ** and each element ainS is invertible with 5-ainS being the inverse of the element a.

For the binary operation * on Z defined by a*b= a+b+1 the identity element is

Find the identity element for the binary operation * on Z defined as a*b = a + b-5. Also find the inverse element of 100.

Find the identity element for the binary operation * on Z defined as a*b = a + b-5. Also find the inverse element of 100.

Prove that the operation ** on ZZ defined by a**b=a|b| for all a,binZZ is a binary operation