# Properties of the equivalence relation

#### paulmdrdo

##### Active member
can you give an example of symmetric property of equality and transitive property of equality. the generalization of these properties are a bit abstract for me. thanks!

#### topsquark

##### Well-known member
MHB Math Helper
Re: Properties of th equivalence relation

can you give an example of symmetric property of equality and transitive property of equality. the generalization of these properties are a bit abstract for me. thanks!
Given a, b, and c
Symmetry: a = b implies b = a

Transitive: (a = b and b = c) implies a = c

Is that what you were looking for?

-Dan

#### paulmdrdo

##### Active member
Re: Properties of th equivalence relation

no. that's the generalize form. i want an example where you can apply the properties.

#### topsquark

##### Well-known member
MHB Math Helper
Re: Properties of th equivalence relation

no. that's the generalize form. i want an example where you can apply the properties.
Are you thinking of something along the lines of
R = {(0, 0), (0, 1), (1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2)}
and then determining if R is symmetric and/or transitive?

-Dan

#### paulmdrdo

##### Active member
Re: Properties of th equivalence relation

yes!

#### HallsofIvy

##### Well-known member
MHB Math Helper
Re: Properties of th equivalence relation

How about "A is equivalent to B if and only if A and B are people and A has the same parents as B".

If A is equivalent to B then A has the same parents as B so that B has the same parents as A: B is equivalent to A.

If A is equivalent to B and B is equivalent to C, then A has the same parents as B and B has the same parents as A. It follows that A has the same parents as C: A is equivalent to C.

#### Evgeny.Makarov

##### Well-known member
MHB Math Scholar
Re: Properties of th equivalence relation

can you give an example of symmetric property of equality and transitive property of equality.
Are you thinking of something along the lines of
R = {(0, 0), (0, 1), (1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2)}
and then determining if R is symmetric and/or transitive?
Hmm. OP, you seem to ask not for an example of a property of equality, but for an example of equality, and, in fact, not of equality, but of an arbitrary relation. I know what an example of an object (e.g., a car) is and what an example of an object with some property (e.g., a red car) is, but I don't know what an example of a property is (what is an example of red?). Formulating your questions precisely is half the answer.