Question 1:

(a) Describe a binary operation on a set S.

(b) Give the definition of a group.

(c) State whether the following statements are TRUE or FALSE. Justify your answer.

(i) The set of natural numbers is closed with respect to multiplication.

(ii) The set of integers is closed with respect to division.

(iii) The set of rational numbers contains the additive inverse for each of its members.

Question 2: Euclidean Algorithm

(a) Explain how the Euclidean algorithm is used to calculate the greatest common divisor of two integers a and b.

(b) Under which condition does the equation ax + by = d, where a,b,c ,a,b ≠ 0, has solution in

(c) Find x, y such that 2431x + 1324y = 11.