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

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

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

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

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 the composition of functions (o) defined on the S={f_1,\ f_2,\ f_3,\ f_4} of four functions from C (the set of all complex numbers) to itself, defined by f_1(z)=z ,\ \ f_2(z)=-z ,\ \ f_3(z)=1/z ,\ \ f_4(z)=-1/z for all z in Cdot

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

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)

Consider the set S={1,\ 2,\ 3,\ 4} . Define a binary operation * on S as follows: a*b=r , where r is the least non-negative remainder when a b is divided by 5. Construct the composition table for * on Sdot

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) .

Construct a frequency table for the following data: (i) 6,7,5, 6, 8, 9, 5, 5, 6, 7, 8, 9, 8, 10, 10, 9, 8, 10, 5, 7, 6,8 (ii) 3,2,1,5, 4, 3, 2, 5, 5, 4, 2, 2, 2, 1,4,1,5,4