Question

Consider the relation S(x, y) : x is a brother or sister of y on the set, H, of living humans. (For the purposes of this problem, a sibling of a person means another person with the same two parents, so don’t consider half siblings.) Determine which of the three properties, reflexive, symmetric, transitive, hold for the relation S (explain your three answers). Is S an equivalence relation on H?

Answer 1

- Not reflexive

- Symmetric

- Transitive

Explanation:

- A person is not a sibling of himself so the relation is NOT reflexive

- If a person is a sibling of an other person, the other person is a sibling of the person. Therefore the relation is SYMMETRIC

- If a person A is a sibling of B, and a person B is a sibling of C then, person A is a sibling of person C. Therefore the relation is TRANSITIVE.