0:00
Hello.
00:01
So for part a, to prove that r here is a equivalent relation, well, first we have that a is going to be related to a.
00:10
So that's going to be reflective because we have 7a minus, again, we have here that 7a minus 5a, which is going to be equal to 2a, which is even.
00:25
So again, a is related to a for all a in the integer.
00:30
So therefore we have that our.
00:32
Is reflexive and then we want to sew that we're symmetric so that means that if a is related to b well then we have that 7a minus 5b is even so therefore we get 12b minus 12 a 12b minus 12 a plus 7a minus 5b is going to be even in other words we have that 7b minus 5 a is even so we have that if a is related to b then b is related to a.
01:16
So if a is related to b, that implies that b is related to a, so we are symmetric.
01:29
And we're also transitive.
01:31
So if we let a being related to b and b related to c, in other words, we have 7a minus 5b and 7b minus 5c are even, then we have that 7a minus 5b plus 7b minus 5c is even.
01:45
So we have 7a minus 5c plus 2b is even, which gives us that 7a minus 5c is even.
01:52
So a is related to c.
01:53
So if we have that a related to b and b related to c, if a is related to b and b is related to c, that implies that a is related to c, so we are transitive...