Write the composition table for the binary operation multiplication modulo `10\ (xx_(10))` defined on the set `S={1,\ 3,\ 7,\ 9}` .

Write the composition table for the binary operation multiplication modulo 10\ (xx_(10)) on the set S={2,\ 4,\ 6,\ 8} .

Write the composition table for the binary operation xx_5 (multiplication modulo 5) on the set S={0,\ 1,\ 2,\ 3,\ 4} .

For the binary operation multiplication modulo 5\ (xx_5) defined on the set S={1,\ 2,\ 3,\ 4} . Write the value of (3xx_5 4^(-1))^(-1) .

Write the multiplication table for the set of integers modulo 5.

Write the inverse of 5 under multiplication modulo 11 on the set {1, 2, ....., 10}.

For the binary operation xx_(10) on set S={1,\ 3,\ 7,\ 9} , find the inverse of 3.

Consider the set S={1,\ -1} of square roots of unity and multiplication (xx) as a binary operation on S Construct the composition table for multiplication (xx) on S Also, find the identity element for multiplication on S and the inverses of various elements.

Construction a composition table for binary operation ^^ defined as a ^^ b = minimum of {a,b} in the set {1,2,3,4,5} and (i) evaluate (2 ^^ 3) ^^4 and 2^^ (3^^ 4)

Write the identity element for the binary operation * defined on the set R of all real numbers by the rule a*b= (3a b)/7 for all a ,\ b in Rdot

Construct the composition table for xx_4 on set S={0,\ 1,\ 2,\ 3} .