I'm struggling to understand binary relations in discrete mathematics. Was hoping that someone would elaborate a few things for me using these questions so I can get better.
Let A be {a,b,c}. Let the relation R be {(a,c),(b,c),(c,c)}.
I understand why this is not symmetric or reflexive because (c,a) !E R and (a,a) !E R. But why is this transitive?
I have one other question that has been bugging me; A=N, for a,b ∈ N: (a, b) ∈ R if and only if a=b
Also, I can see why this is reflexive, but how can it be symmetric and transitive? I think I have some gaps in my knowlege because I am assuming R would look something like R = {(a,a),(b,b),(c,c)...}
Let A be {a,b,c}. Let the relation R be {(a,c),(b,c),(c,c)}.
I understand why this is not symmetric or reflexive because (c,a) !E R and (a,a) !E R. But why is this transitive?
I have one other question that has been bugging me; A=N, for a,b ∈ N: (a, b) ∈ R if and only if a=b
Also, I can see why this is reflexive, but how can it be symmetric and transitive? I think I have some gaps in my knowlege because I am assuming R would look something like R = {(a,a),(b,b),(c,c)...}