Q11 of 123 Page 3

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

From the definition of multiplication modulo

a*b = (m is the base of the modulo)

And here the base is 3 and the set is S = {2,4,6,8}.

So, the composition table can be formed as :-

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

Define identity element for a binary operation defined on a set.

For the binary operation multiplication modulo 10(×₁₀) defined on the set S = {1, 3, 7, 9}, write the inverse of 3.

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

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