Question

need help in understanding transitive relations

Answer 1

> Not allowed:
>
> • "Do this for me" posts
>
> • one-sentence posts (Have some respect for people who take time to answer your question and follow the posting rules.)

In other words, tell us what you have tried and what's holding you back.

Answer 2

To be transitive, the following has to be true:

**If** (a,b) and (b,c) are in the relation, **then** (a,c) must be in the relation.

For 1,2,3,  and P,  that statement is true.   If you think it's not true, then you must have a specific example where (a,b) and (b,c) are in the relation but where (a,c) is not in the relation.    

For Q it is not true.  (1,2) and (2,3) are in the relation but (1,3) is not.

Answer 3

To be transitive, consider all possible pairs of two inputs of the form  (a,b) and (b,c).   The a, b and c don't have to be distinct, but the b's have to be the same, thus they are both called b.

If you have (a,c) in your relation for all such pairs, then your relation is transitive.  This includes the case when you have no such pairs, in which case it is vacuously true.

Answer 4

For #1, what are all the elements that 1 relates to?

Answer 5

thank you everyone, i finally understand it now

I'm sorry for being rude.