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Question -

For the binary operation ├Ч10 set S = {1, 3, 7, 9}, findthe inverse of 3.



Answer -

Here,

1 ├Ч10 1= remainder obtained by dividing 1 ├Ч 1 by 10

= 1

3 ├Ч10 7= remainder obtained by dividing 3 ├Ч 7 by 10

= 1

7 ├Ч10 9= remainder obtained by dividing 7 ├Ч 9 by 10

= 3

So, the compositiontable is as follows:

├Ч10

1

3

7

9

1

1

3

7

9

3

3

9

1

7

7

7

1

9

3

9

9

7

3

1

From the table we canobserve that elements of first row as same as the top-most row.

So, 1 тИИ S is the identity element with respect to ├Ч10

Now we have to findinverse of 3

3 ├Ч10 7= 1

So the inverse of 3 is7.

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