Fsc Part 1 Mathematics (Complete Solution)

Q3
Show that the adjointing table is that of multiplication of the elements of the set of residue classes modulo 5.

* 0 1 2 3 4
0 0 0 0 0 0
1 0 1 2 3 4
2 0 2 4 1 3
3 0 3 1 4 2
4 0 4 3 2 1

Solution:

The zeros in the second column and the second row are produced by the 0 in the first column and the second row which show that this is a product table, because zero when multiplied any number wil again be zero.Now every element in the table is lesser than 5, so the table is a multiplication table of the elements of the set of residue classes module 5. clearly {0,1,2,3,4} is the set of residues.

thus 3 x 2 = 6 but in place of 6 we insert 1(=6-5).

similarly , in place of 2 x 4 = 8 we insert 3(=8-5) in the table.

* 0 1 2 3 4
0 0 0 0 0 0
1 0 1 2 3 4
2 0 2 4 6  8
3 0 3 1 4 2
4 0 4 3 2 1

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