# NIELIT 2017 DEC Scientist B - Section B: 48

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On a set $A = \{a,b,c,d\}$ a binary operation $*$ is defined as given in the following table.

$$\begin{array}{|c|cccc|}\hline\text{*}&a&b&c&d\\\hline \text{a}&a&c&b&d\\\text{b}&c&b&d&a\\\text{c}&b&d&a&c\\\text{d}&d&a&c&b\\\hline \end{array}$$

The relation is:

- Commutative but not associative
- Neither commutative nor associative
- Both commutative and associative
- Associative but not commutative

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