Question -
Answer -
(a) Is * both associative and commutative?
(b) Is * commutative but not associative?
(c) Is * associative but not commutative?
(d) Is * neither commutative nor associative?
Solution
On┬аN, the operation *is defined as┬аa┬а*┬аb┬а=┬аa3┬а+┬аb3.
For,┬аa,┬аb,тИИ┬аN, we have:
a┬а*┬аb┬а=┬аa3┬а+┬аb3┬а=┬аb3┬а+┬аa3┬а=┬аb┬а*┬аa┬а[Addition is commutative in┬аN]
Therefore,the operation * is commutative.
Itcan be observed that:
тИ┤(1 * 2) * 3 тЙа 1 * (2 * 3) ; where 1, 2, 3 тИИ┬аN
Therefore,the operation * is not associative.
Hence,the operation * is commutative, but not associative. Thus, the correct answeris B.