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

Let ** be an operation defined on A,={2,4,6,8} by a**b=k where k is the least non-negative remainder when the product ab is divided by 10 and a,binA. show that ** is a binary operation on A.

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 least non-negative remainder when product is divided by 5. Prove that * is a binary operation on Sdot

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 .

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

Let A={0,1,2,3,4,5}. If a_(1)binA, then an operation @ on A is defined by a@b=k where k is the least non-negative remainder when the sum (a+b) is divided by 6. Show that @ is a binary operation on A.

Let S={0,1,2,3,4}, if a,binS , then an operation ** on S is defined by, a**b=r where r is the non-negative remaider when (a+b) is divided by 5. Prove that ** is a binary operation on S.