question_answer 47)

Consider the binary operation * on the set {1, 2, 3, 4, 5} given by the following multiplication table(Table) (i)     Compute (2 * 3) * 4 and 2 * (3 * 4) (ii)    Is * commutative ? (iii)   Compute (2 * 3) * (4 * 5) (Hint: Use the following Table).

*	1	2	3	4	5
1	1	1	1	1	1
2	1	2	1	2	1
3	1	1	3	1	1
4	1	2	1	4	1
5	1	1	1	1	5

 

Answer:

(i) (2*3) * 4 = 1 * 4 = 1 and 2 * (3 * 4) = 2 * 1 = 1 Clearly (2 * 3) * 4 = 2 * (3 * 4) (ii) Since the given composition is symmetrical about the diagonal of multiplication table, therefore* is commutative. (iii) (2 * 3) * (4 * 5) = 1 * 1 = 1.