Let A = {1, 2, 3, 4, 5, 6}. Which statement below is true? (Hint: The equivalence classes of an equivalence relation on A gives a partition of A, or in other words, their union is A and they are pairwise disjoint.) There is an equivalence relation on A whose equivalence classes are: {1,2},{3,5}, {6}. There is an equivalence relation on A whose equivalence classes are: {1,2, 3}, {3, 5}, {4,6}. There is an equivalence relation on A whose equivalence classes are: {1,2,3}, {5}, {5,6}. There is an equivalence relation on A whose equivalence classes are: {1,2, 3}, {5}, {4,6}.

Question 2 List all possible equivalence relations on the set {1,2,3,4} without repetition up to isomorphism. Justify your answer.

please answer number 7. If you can please answer as much as you can.

You just bought a new car from a dealership that sells cars no older than 2015. Consider therelationship 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

Prove or disprove the following statements

Let S be a nonempty set. Consider the relation ~ on P(S) defined by A ~ B if AUBC = S. Is the relation an equivalence relation? Explain. If yes, identify (no need to justify) the equivalence class of

I am having trouble working thru this problem, any help would be appreciated.