1. ## Equivalence Relations

Question:

Suppose R is the relation on N where aRb means that a ends in the same digit in which b ends. Determine whether R is an equivalence relation on N.

2. Originally Posted by oldguy
Question:

Suppose R is the relation on N where aRb means that a ends in the same digit in which b ends. Determine whether R is an equivalence relation on N.
do you recall what an equivalence relation is? you must show whether or not the relation described is reflexive, symmetric and transitive. if it is, it is an equivalence relation

3. Do I create an equation by which the relationship of a and b ends in the same digit? Then define a matrix to prove the reflexive, symmetric and transitive properties?

I am not sure how to proceed.

4. Originally Posted by oldguy
Do I create an equation by which the relationship of a and b ends in the same digit? Then define a matrix to prove the reflexive, symmetric and transitive properties?

I am not sure how to proceed.
...where did you get matrix from? we have a relation on the integers. we have an element a relating to an element b if they end in the same digit. now see if such a relationship is reflexive, symmetric and transitive

can you continue?

5. Is the question talking about one value for "a" and one value for "b" that ends with the digit? If so, then it is definately reflective if the values for "a" and "b" both =5. It is not symmetric and not transitive. Am I on the right track?

6. Originally Posted by oldguy
Is the question talking about one value for "a" and one value for "b" that ends with the digit? If so, then it is definately reflective if the values for "a" and "b" both =5. It is not symmetric and not transitive. Am I on the right track?
why do you say it is not symmetric? not transitive?

do you remember what the definitions of symmetric and transitive are?

7. Symmetric a|b b|a. It is symmetric. Not sure how you could prove it is or is not transitive ( a|b b|c a|c )?

8. Originally Posted by oldguy
Symmetric a|b b|a. It is symmetric. Not sure how you could prove it is or is not transitive ( a|b b|c a|c )?
yes, it is symmetric. for transitive, consider this: a,b, and c are integers. if a and b end with the same digit, and b and c end with the same digit, does it mean that a and c end with the same digit?

9. Yes!

10. Originally Posted by oldguy
Yes!
ok, so it is transitive then. that wasn't so hard, was it?