Consider the set `S={1,\ -1,\ i ,\ -i}` of fourth roots of unity. Construct the composition table for multiplication on `S` and deduce its various properties.

Consider the set S={1,-1,i ,-i} for fourth roots of unity. Construct the composition table for multiplication on S and deduce its various properties.

Consider the set S={1,\ omega,\ omega^2} of all cube roots of unity. Construct the composition table for multiplication (xx) on Sdot Also, find the identity element for multiplication on Sdot Also, check its commutativity and find the identity element. Prove that every element of S is invertible.

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.

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

Construct the composition table for +_5 on set S={0,\ 1,\ 2,\ 3,\ 4} .

Construct the composition table for xx_5 on Z_5={0,\ 1,\ 2,\ 3,\ 4} .

Construct the composition table for xx_6 on set S={0,\ 1,\ 2,\ 3,\ 4,\ 5} .

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 xx_5 (multiplication modulo 5) on the set S={0,\ 1,\ 2,\ 3,\ 4} .

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