00:01
Hello, so you're starting with the first one.
00:04
Now, ab belongs to z.
00:08
We have to show that b divides a if and only if minus b divides a.
00:16
Now, b divides a implies b will be equal to ma where m belongs to z.
00:25
We'll say that multiply by minus 1.
00:33
Minus b will be minus 1 into ma.
00:38
This will be minus m into a.
00:41
That means minus b will divide a as this can be written as n into a where n minus m is equal to n.
00:59
Therefore, first statement is correct.
01:01
Now, if minus b divides a implies minus b is equal to sa where s belongs to z.
01:16
We will multiply by minus 1.
01:19
So, b will be equal to ta where t is equal to minus s and t belongs to z.
01:30
This implies b divides a and hence, prove.
01:40
Further, now we have to prove the second part for this.
01:48
That means a union b complement will be, we have to prove a intersection b complement is equal to a complement intersection b complement.
02:10
We'll say that let us take x belongs to a union b the whole complement...