At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

Consider a relation on the set of all states in the United States given by: two states are related if they have a border in common. Is it an equivalence relation

Sagot :

Answer:

Yes it is an equivalence relation

Explanation:

An equivalence relation is a binary relation between two values that are symmetric, transitive and reflexive. In other words, when we say a value x is equal(using "=") to a value y, there is an equivalence relation between them.

Example, given set {x, y, z} where ~ means equivalence:

x ~ y if y ~ z means symmetric

since x ~ y and y ~ z, then x ~ z means transitive

x ~ x means reflexive

Equivalence relations share a common attribute or attributes(example, a satisfying condition)

The above condition that two states are related from the set of all US states if they have a border in common satisfies the condition of equivalence listed hence it is an equivalence relation.