Relations - Reflexive, Symmetric, Transitive

Question

I have the following question and corresponding answers, but I cannot quite understand how it works. Can anyone describe to me in plain English the reason why these relations are reflexive, symmetric, or transitive.

Determine which of the following relations on the set of people is reflexive? symmetric? transitive?

(a) has the same parents as (b) is a brother of (c) is older or younger than

Thanks!

Answer 1

EDIT: The original question has been changed, so my answer refers to the question "is the relation 'has the same parents as' symmetric, reflexive, or transitive?"

Let A, B, and C be people.

For part a):

Symmetric: If A has the same parent as B, then does B has the same parents as A? Yes, so it is symmetric.

Reflexive: Does A have the same parents as A? Obviously yes, so it's reflexive.

Transitive: If A has the same parents as B, and B has the same parents as C, then does A have the same parents as C? Yes, so it is transitive.

Can you figure out b) and c)?