What kind of relation is this?

Question

A person can remember himself at different points in the past. Each of 'himself' that he remembers at each point in the past can also remember a person in the past, and so on.

So if we have a, b, c, d

So

• c has a direct relation to d
• b has a direct relation to c and to d
• b has another relation to d via c
• a has a direct relation to b, to c, and to d
• a has another relation to c via b, and to d via b, and to d via b via c

EDIT: Another example would be a military chain of command - The General can command the Colonel directly, and he can command the Private directly, and he can command the Private by way of commanding his Colonel.

What relations would describe the relation in the example?

Answer 1

Let's call the relation $R$, and the relations we have are $cRd, bRc, bRd, aRb, aRc, aRd$. So, by inspection the relation is transitive.

Answer 2

The question is asking you to test this relation against the types you know. One is probably reflexive. This requires that for all elements $x$ of the set, we have $xRx$. As we do not have $aRa$, it is not reflexive. Some other types might be symmetric, antisymmetric, transitive, partial order, total order. Look up the definitions and see.