00:01
Now, in this question, we look at equivalence relation, right? suppose this represents an equivalence relation, right? and this basically says x and y are equivalent if and only if x, y are larger than zero, okay? only if x, y, like than zero, or if x equals y equals zero, right? so this is a equivalent relation, and the reason why this is an equivalence relation is very simple, right? because this relation is transitive.
00:28
In other words, if x and y are equivalent and the and where and z also equivalent, then we can be sure that x and z equivalent.
00:37
Because what this equivalent relation, what it actually means is that x, y must have the same sign, right? they could have the both be positive sign or both be negative sign or both be zero, right? so if x, y, y, z have the positive sign and y, z have the same sign, then obviously x and z must have the same sign as well, right? so that's basically what is the equivalent.
00:58
Relation means, right? if x and y have the same sign and one and z have the same sign, then x z, x and z must have the same sign.
01:05
So in other words, this relation is transitive.
01:08
So it is a equivalence relation, right? and so what are the equivalence classes? well, as i said, there are three, actually, there are three equivalency classes...