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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!

user3371750
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1 Answers1

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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)?

Bonnaduck
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  • Thanks Bonnaduck, my answers would therefore be the following:

    b) is a brother of:

    Symmetric: If A is a brother of B, then B is a brother of A. Therefore it is symmetric.

    Reflexive: A cannot be a brother of itself, therefore it is not reflexive.

    Transitive: If A is a brother of B, and C is a brother of B, then A is a brother of C. It is transitive.

    However in my textbook it says that this is not symmetric?

     – user3371750 May 15 '14 at 21:30
  • c) is older or younger than:

    Symmetric: If A is younger than B, then B is older than A. It is symmetric.

    Reflexive: A cannot be older/younger than itself. Not reflexive.

    Transitive: If A is older than B, and B is older than C, then C is younger than A. It is transitive.

    My textbook also says that this relation is not transitive?

     – user3371750 May 15 '14 at 21:31
  • For b), if A is a boy, and B is a girl, then B is a sister of A, not a brother. So it is not symmetric. For c), A and C could be the same age, so it is not transitive. – Bonnaduck May 15 '14 at 21:40