(A) Is * both associative and commutative? (B) Is * commutative but not associative? (C) Is * associative but not commutative? (D) Is * neither commutative nor associative?

(i) For an arbitrary binary operation * on a set N, a * a = a  . (ii) If * is a commutative binary operation on N, then a ...

(i) a * b = a–b (ii) a * b = (iii) a * b = a + ab (iv) a * b =

(i) 5 * 7,  20 * 16 (ii) Is * commutative? (iii) Is * associative? (iv) Find the identity of * in N (v) Which elements of N are invertible for the operation * ?

(i) Compute (2*3)*4 and 2*(3*4) (ii) Is * commutative? (iii) Compute (2*3)*(4*5). (Hint: use the following table)