# Relation ( Equivalence Relation)

• Dec 3rd 2008, 01:38 PM
bhuvan
Relation ( Equivalence Relation)
Which of these relation on the set of all people are equivalence relation ? Determine the properties of an equivalence relation that the other lack.

(1) {(a,b) | a and b are the same age}
(2) {(a,b) | a and b have the same parents}
(3) {(a,b) | a and b share a common parents}
(4) {(a,b) | a and b have met}
(5) {(a,b) | a and b speak common language}

• Dec 3rd 2008, 02:05 PM
Plato
Why don’t you show us some of your own work on these?
Here is a hint. Often such words as “equal or the same as” point to an equivalence relation.
But be careful, for #2 & #3 look a lot alike, however one is an equivalence relation and the other is not.
• Dec 3rd 2008, 03:30 PM
bhuvan
I do not even know how to begin or solve this otherwise i would have showed you some of my work.
• Dec 3rd 2008, 04:40 PM
bhuvan
As far as i understand (1) and (2) are Equivalence Relation but i am not sure about the other ones that are they reflexivity,symmetry and transitive.

• Dec 3rd 2008, 06:01 PM
Plato
Go and have a sit-down with your lecturer/teacher/instructor.
Tell that person just how much you do not understand.
Having done that and if you still do not understand any of this then drop the course.
• Dec 3rd 2008, 11:02 PM
anjaneyaindia
Quote:

Originally Posted by bhuvan
Which of these relation on the set of all people are equivalence relation ? Determine the properties of an equivalence relation that the other lack.

(1) {(a,b) | a and b are the same age}
(2) {(a,b) | a and b have the same parents}
(3) {(a,b) | a and b share a common parents}
(4) {(a,b) | a and b have met}
(5) {(a,b) | a and b speak common language}

(4) is not reflexive so not eqivalence
(5)5 is also equivalent relation
• Dec 4th 2008, 12:26 AM
clic-clac
I meet myself every morning in my mirror (I guess the answer depends on what means to meet ;)); what is sure is that (4) isn't transitive. (If a friend of you knows somebody, that doesn't mean you also know him/her)

(5) is reflexive, symmetric, but... if I speak french, my friend speaks french and spanish, and another guy speaks only spanish, transitivity is dead.

Of course the problem when you want to apply mathematical definitions to "real" cases is that real cases must be very well defined to avoid ambiguity (i.e. I may have done wrong)
• Dec 5th 2008, 12:04 AM
anjaneyaindia
Look at this similar example, but purely mathematic: $\forall a,b\in \mathbb{N},\ aRb \Leftrightarrow a,b$ have a common prime divisor.
$3R6$ , $6R2$ , but $pgcd(2,3)=1$, so we don't have $2R3$.