00:01
Hi there, in this question we need to just write the addition and multiplication tables for z sub 6.
00:06
So z sub 6 sat contains the number from 0, 1, 2, 3, 4 and 5.
00:15
So z sub 6 means the remainders when you just divide the number by 6, the remainders would be 0 from 0 to 5.
00:27
So what we have to do, we have to just make an addition table.
00:32
So for the addition table, let me just write here.
00:35
So we need to one row and one column.
00:38
So we know that this is zero, one, two, three, four, and five.
00:43
And for the column, it is zero, one, two, three, four, and five.
00:51
So for the addition, we are going to just add numbers.
00:54
If the addition is greater than six, we need to just.
00:58
Divide by six and get the remainder.
01:00
For example, 0 plus 0, which is 0, and 0 plus 1, which is 1, 1 is less than 6.
01:07
So i can write 1 .0 plus 2, 2, 0 plus 3, 0 plus 4, 4, and 0 plus 5, 5.
01:15
So 1 plus 0, 1, 1 plus 1, 2, 1 plus 2, 1 plus 2, 3, 1 plus 4, 5, 6.
01:25
If we divide 6 by 6, we will get the remainder as 0, so i'm going to put as 0 here.
01:31
2 plus 0, i mean 2 plus 0 2, 2 plus 1, 3, 2 plus 4, 2 plus 2 plus 2, 4, 2 plus 2 plus 4, 2 plus 2, 2 plus 4, 2 plus 2, 2 2 again...