Let `S=(0,1,2,3,4,)` and * be an operation on S defined by `a*b=r` , where`r` is the least non-negative remainder when `a+b` is divided by 5. Prove that * is a binary operation on S.

Let S=(0,1,2,3,4,) and * be an operation on s defined by a*b=r, wherer is the least non-negative remainder when a+b is divided by 5. Prove that * is a binary operation on S .

Let S={1,2,3,4} and * be an operation on S defined by a*b=r, where r is the least non-negative remainder when product is divided by 5.Prove that * is a binary operation on S.

Let S={1,2,3,4} and * be an operation on S defined by a*b=r, where r is the last non- negative remainder when product is divided by 5.Prove that * is a binary operation on S .

On the set W of all non-negative integers * is defined by a*b=a^(b) .Prove that * is not a binary operation on W.

Let r be the least non-negative remainder when (22)^(7) is divided by 123. The value of r is

Consider the set S={1,2,3,4}. Define a binary operation * on S as follows: a*b=r, where r is the least non-negative remainder when ab is divided by 5. construct the composition table for * on S.

Is * defined by a^(*)b=(a+b)/(2) is binary operation on Z.

Let * be a binary operation defined by a*b=3a+4b-2. Find 4^(*)5

If a binary operation is defined by a**b = a^b then 4**2 is equal to:

If a binary operation is defined by a**b=a^(b) , then 3**2 is equal to :