(A) Is * both associative and commutative? (B) Is * commutative but not associative? (C) Is * associative but not commutative? (D) Is * neither commutative nor associative?
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(i) For an arbitrary binary operation * on a set N, a * a = a . (ii) If * is a commutative binary operation on N, then ...
(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)
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