Define a binary operation on a set.

Define a binary operation * on the set A={0,\ 1,\ 2,\ 3,\ 4,\ 5} as a * b=a+b(mod 6) Show that zero is the identity for this operation and each element a of the set is invertible with 6-a being the inverse of adot

Define a binary operation * on the set A={0,1,2,3,4,5} as a*b=a+b (mod 6). Show that zero is the identity for this operation and each element a of the set is invertible with 6-a being the inverse of adot OR A binary operation * on the set {0,1,2,3,4,5} is defined as a*b={a+b ,ifa+b<6a+b-6,ifa+bgeq6 Show that zero is the identity for this operation and each element a of set is invertible with 6-a , being the inverse of a.

Define a binary operation * on the set A={0,1,2,3,4,5} as a*b=a+b (mod 6). Show that zero is the identity for this operation and each element a of the set is invertible with 6-a being the inverse of adot OR A binary operation * on the set {0,1,2,3,4,5} is defined as a*b={a+b ,ifa+b<6a+b-6,ifa+bgeq6 Show that zero is the identity for this operation and each element a of set is invertible with 6-a , being the inverse of a.

Define a binary operation * on the set A={0,1,2,3,4,5} given by a\**b=a b (mod 6) . Show that 1 is the identity for *. 1 and 5 are the only invertible elements with 1^(-1)=1 and 5^(-1)=5

Define a binary operation * on the set A={0,1,2,3,4,5} given by a*b=a b (mod 6). Show that 1 is the identity for *. 1 and 5 are the only invertible elements with 1^(-1)=1 and 5^(-1)=5

Define a binary operation ** on the set A={1,\ 2,\ 3,4} as a**b=a b\ (mod\ 5) . Show that 1 is the identity for ** and all elements of the set A are invertible with 2^(-1)=3 and 4^(-1)=4.

Define a binary operation ** on the set {0, 1, 2, 3, 4, 5} as a**b={a+b if a+b<6; a+b-6,if a+b geq 6 . Show that zero is the identity for this operation and each element a !=0 of the set is invertible with 6-a being the inverse of a

Define a commutative binary operation on a set.

Define an associative binary operation on a set.

A binary operation is chosen at random from the set of all binary operations on a set A containing n elements. The probability that the binary operation is commutative, is