Consider the binary operation* on the set {1, 2, 3, 4, 5} defined by a * b=min. {a, b}. Write the operation table of the operation *.

Consider the binary operation ^^ on the set {1,quad 2,quad 3,quad 4,quad 5} defined by a^^b operation table of the operation ^^ .

Consider the infimum binary operation ^^ on the set S={1,2,3,4,5} defined by a^^b= Minimum of aandb .Write the composition table of the operation ^^ .

If the binary operation * on the set Z of integers is defined by a*b=a+b-5 then write the identity element for the operation * in Z .

Let *prime be the binary operation on the set {1," "2," "3," "4," "5} defined by a*primeb=" "HdotCdotFdot of a and b. Is the operation *prime same as the operation * defined in Exercise 4 above? Justify your answer.

If the binary operation ** on the set Z of integers is defined by a**b=a+b-5 , then write the identity element for the operation '**' in Z.

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 .

If the binary operation * on the set Z of integers is defined by a*b=a+3b^(2), find the value of 2*4.

If the binary operation * on the set of integers Z, is defined by a^(*)b=a+3b^(2), then find the value of 2*4

If the binary operation * on the set Z of integers is defined by a*b=a+3b^(2), find the value of 2*4.

Consider the binary operation on Z defined by a ^(*)b=a-b . Then * is