Login/Sign Up
Home » Construct the composition table for on set S = {0, 1, 2, 3, 4, 5}.
Construct the composition table for \times_6 on set S = {0, 1, 2, 3, 4, 5}.
Binary Operations | CBSE | Class 12 | Exercise 3.5 | Maths | RD Sharma
Construct the composition table for \times_6 on set S = {0, 1, 2, 3, 4, 5}.

Solution:

Here,
1 \times_{6} 1= remainder obtained by dividing 1 \times 1 by 6
=1
3 \times_{6} 4= remainder obtained by dividing 3 \times 4 by 6
=0
4 \times_{6} 5= remainder obtained by dividing 4 \times 5 by 6
=2
Therefore, the composition table is as follows:

    \[\begin{tabular}{|l|l|l|l|l|l|l|} \hline$\times_{6}$ & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline 1 & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline 2 & 0 & 2 & 4 & 0 & 2 & 4 \\ \hline 3 & 0 & 3 & 0 & 3 & 0 & 3 \\ \hline 4 & 0 & 4 & 2 & 0 & 4 & 2 \\ \hline 5 & 0 & 5 & 4 & 3 & 2 & 1 \\ \hline \end{tabular}\]

i

More Material