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Properties of the equivalence relation

paulmdrdo

Active member
May 13, 2013
386
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
Aug 30, 2012
1,123
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
May 13, 2013
386
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
Aug 30, 2012
1,123
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
May 13, 2013
386
Re: Properties of th equivalence relation

yes!
 

HallsofIvy

Well-known member
MHB Math Helper
Jan 29, 2012
1,151
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
Jan 30, 2012
2,492
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.