The relation on the real numbers R defined by a ~ b if both a > b and b>a is not an equivalence relation. Why not? What properties of an equivalence relation does it satisfy?

What are the equivalence classes of the equivalence relations  (answer d and e)   (DO NOT ANSWER IF THEY ARE EQUIVALENCE RELATIONS OR NOT, THAT IS NOT THE QUESTION) thank you!

Please solve (c) and (d) only, thank you!

Let R and S be any two equivalence relations on a non-empty set A. Then check whether ( R intersection S ) will be a equivalence relation?

R is a relation on set of integers (Z) and it is given by Then, R is (x, y) = R⇒ |x − y| ≤ 1. reflexive and transitive reflexive and symmetric equivalence relation symmetric and transitive

You just bought a new car from a dealership that sells cars no older than 2015. Consider the relationship to be the “same age.” The relation is “same age” and the set is cars made in 2015, 2016, 2017, 2018, 2019, and 2020. (a) Prove that this relation is an equivalence relation. (b) Describe the partition defined by the equivalence classes

I need help answering the attached question.  Thank you

Help me solve this problem.

5 Equivalence relation? A relation on the integers is divided by x~y if and only ifx+2y is divisible by 3. Is this an equivalence relation? If so, describe the equivalence classes of ~. If not, explain why not.