00:01
In this question, we are asked to show that r defy as the following is equivalent relation.
00:08
I define on the set of other pair of positive integer and a b relate to cd even only if a times d equals b times c.
00:25
So we kind of cross, multiply them.
00:29
And we will check three properties to show that it is equivalent relation.
00:38
First is reflexive.
00:40
So ab has to relate to itself.
00:46
And you can see here that it means that we want ab equals to b.
00:52
But since a and b are positive integers, they are equals because it's commutative.
01:00
Like multiplication is commutative.
01:03
So this property is clear next the symmetry so if a a be related to cd we want the reverse to be true so we want cd to relate to ab as well and we can do that by just looking at the definition when a b related to cd we have this equation right this mean that when we we just rearrange them basically we swap swaps and commute them we have cb equal to d a as well right but this is a definition for for when cd related to ab all right uh when you check these kind of property it is important to arrange the position of of entries in here as exactly the same as your definition.
02:12
In this case it doesn't matter because there are integers, right? but when they are like metrics or something that cannot commute, then you have to check carefully.
02:27
Okay, but in this case it's simple.
02:30
This property is clear...