plzzz i needed Q2,3

2. (a) Let S = {a,b,c}. How many closed binary operations * on S are there that satisfy the condition that for all x S we have r * x + x ? [2 marks] (b) Let S be a set of n > 2 elements. How many closed binary operations * on S are there that satisfy the condition that for all x ES we have x*+ ? [3 marks) 3. Consider the binary operation on the set A= {a,b} defined by the table below: a a b b | a Find the multiplication tables for the four binary operations *a, 0q*and of corresponding to , as defined in Exercise 2.12. According to Light's Associativity test, do these tables allow you to conclude whether or not the binary operation is associative? (If they do, explain why and say if is associative, if they do not, explain why not.) [6 marks]