0:00
Hi.
00:01
Now r is a relation defined on set n as arb is equal to either a divides 2b or b divides 2a.
00:12
Now we have to prove or disprove that r is an equivalence relation.
00:22
Now for reflexive, now we consider ara.
00:29
So that is a divides 2a which is very obvious.
00:33
So aa belongs to r.
00:35
So this is reflexive.
00:36
Now for symmetric, we let ab belongs to r and if we show that ba also belongs to r, then it is symmetric.
00:46
So as ab belongs to r, so a divides 2b.
00:49
Let us take this as the first one.
00:52
A divides 2b.
00:54
So this implies 2b is equal to some k times a.
00:57
So this implies b is equal to k by 2 times a which can be written as k by 4 into 2a.
01:02
So this shows that b divides 2a.
01:09
So b divides 2a.
01:10
So this implies that ba belongs to r...
