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paulmdrdo1
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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 cpaulmdrdo 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!
Are you thinking of something along the lines ofpaulmdrdo said:no. that's the generalize form. i want an example where you can apply the properties.
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?
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.paulmdrdo said:yes!
An equivalence relation is a mathematical concept that defines a relationship between elements of a set. It is a binary relation that satisfies three properties: reflexivity, symmetry, and transitivity.
The reflexive property states that every element in a set is related to itself. In other words, for any element a in a set, (a, a) is part of the relation.
The symmetric property states that if two elements a and b are related, then b is also related to a. In other words, if (a, b) is part of the relation, then (b, a) is also part of the relation.
The transitive property states that if two elements a and b are related, and b and c are related, then a and c are also related. In other words, if (a, b) and (b, c) are part of the relation, then (a, c) is also part of the relation.
Equivalence relations are used to classify and group objects based on their properties. They are also used in the construction of mathematical structures such as equivalence classes, quotient sets, and partitions.