MHB Properties of the equivalence relation

AI Thread Summary
The discussion focuses on understanding the symmetric and transitive properties of equality through practical examples. The symmetric property is illustrated by stating that if a = b, then b = a. The transitive property is explained as if a = b and b = c, then a = c. A specific example involving relationships between people with the same parents is provided to clarify these concepts. The conversation emphasizes the importance of formulating questions precisely to facilitate better understanding.
paulmdrdo1
Messages
382
Reaction score
0
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!
 
Mathematics news on Phys.org
Re: Properties of th equivalence relation

paulmdrdo said:
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
 
Re: Properties of th equivalence relation

no. that's the generalize form. i want an example where you can apply the properties.
 
Re: Properties of th equivalence relation

paulmdrdo said:
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
 
Re: Properties of th equivalence relation

yes!
 
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.
 
Re: Properties of th equivalence relation

paulmdrdo said:
can you give an example of symmetric property of equality and transitive property of equality.

topsquark said:
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?

paulmdrdo said:
yes!
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.
 
Back
Top