00:01
In the given equation, relation r is defined as x, y such that x -y is an integer.
00:12
It is an integer.
00:15
Now, first of all, let any x, y belongs to r.
00:23
X, y, z belongs to r, real number.
00:27
Therefore, x -x equals to 0, which is integer.
00:35
Here, 0 is integer.
00:38
Therefore, this implies x, x belongs to r.
00:45
Then, next, therefore, since x, x belongs to r, therefore, r is reflexive.
00:55
R is reflexive.
00:57
Then, next, let us assume, let us assume x, y, x, y belongs to r.
01:10
Therefore, therefore, x -y is integer.
01:16
X -y is integer.
01:20
Similarly, similarly, y -x is integer because x, y are also integer.
01:30
So, y -x is also integer.
01:34
This implies y, x also belongs to r.
01:40
Therefore, r is symmetric.
01:43
Therefore, r is symmetric because x, y belongs to r and y, x also belongs to r...