Re: Relation From Set A to B

Re: Relation From Set A to B

Quote:

Originally Posted by

**Bashyboy** {(1,3), (1,4), (2,3), (2,4), (3,1), (3,4)}

According to the answer key, it has none of the properties. I was thinking it was perhaps antisymmetric and transitive. Why isn't it so?

(1, 3) and (3, 1) are in the relation. This pertains to both transitivity and antisymmetry.

Quote:

Originally Posted by

**Soroban** What is the GCD of 0 and 0?

Both 0 and 0 are divisible by

. . Hence:

.

Rather, 0 and 0 do not have the *greatest* common divisor because any number is a divisor.

Quote:

Originally Posted by

**Bashyboy**

A stylistic remark: In this case, instead of "*a* ∈ A and *b* ∈ B," it should say "*a* ranges over A and *b* ranges over B." The former phrase raises questions whether you are talking about some specific *a* and *b* that you forgot to introduce or you are considering some arbitrary *a* and *b* and, if so, for what reason. The latter phrase means that whenever *a* is used in what follows, the reader may assume that it is some element of A.

Re: Relation From Set A to B

So, are you saying that, perhaps, the answer key is wrong; and that {(1,3), (1,4), (2,3), (2,4), (3,1), (3,4)} is transitive and antisymmetric?

Also, thank you for your last remark, concerning the phrasing of certain things.

Re: Relation From Set A to B

Quote:

Originally Posted by

**Bashyboy** So, are you saying that, perhaps, the answer key is wrong; and that {(1,3), (1,4), (2,3), (2,4), (3,1), (3,4)} is transitive and antisymmetric?

No, the answer key is correct, and you can build counterexamples using (1, 3) and (3, 1).