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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:

  1. Commutative but not associative
  2. Neither commutative nor associative
  3. Both commutative and associative
  4. Associative but not commutative

NIELIT 2017 Scientist B - Section B-48

in Set Theory & Algebra by Veteran
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3 Answers

+1 vote
Commutative but not associative

ex.for associative  a*(b*d) = a*a = a

(a*b)*d =c*d =c
by Boss
+1 vote
$A$  is correct.

Work through some examples. Like  $a*b=b*a=c$,  $c*b=b*c=d$ and so on.

It is not associative w.r.t this example:   $(a*b)*c=c*c=a$  but $a*(b*c)=a*d=d$,  which are not equal.
by Active
0 votes
(A) Commutative but not associative
by Junior

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