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 a.

Define a binary operation * on the set A={1,2,3,4} as a*b=ab(mod5) 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 A={1,2,3,4} as a^(*)b=ab(mod5). 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""geq6 Show that zero is the identity for this operation and each element a !=0 of the set is invertible with 6 a being t

Define a binary operation * on the set A={0,1,2,3,4,5} given by a*b=ab(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} 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 a . OR A binary operation ** on the set {0,1,2,3,4,5} is defined as a**b={[a+b if a+b = 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 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

Determine whether * on N defined by a*b=a^(b) for all a,b in N define a binary operation on the given set or not: