For the set A = {are, bot, cab, era)}, define the relation R on A to be: (x,y) eR if and only if word x and word y share one letter only. For example (are, cab) is in R because those words share one letter only ("a"). But (are, era) is NOT in R because those words do NOT share one letter only, they share 3 letters. Also (bot, era) is NOT in R since they share no letters at all. In cach part, answer yes or no. If yes, then explain why in terms of this specific relation about sharing letters (not just by stating the generic definition of the property). If you say a) Is R reflexive? b) Is R symmetric? c) Is R antisymmetric? d) Is R transitive?

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A car dealership sells cars that were made in 2015 through 2020. Let the cars for sale be the domain of a relation R where 2 cars are related if they were made in the same year. b) Describe the partition defined by the equivalence classes. How do I do this?

5) What is the cardinality of the set {characters in set A}? 6) Let X = {strings in A}. Find |X 7) Let X {strings in A} Name two B, CC X and two D, ECX such that... a) BUC X B = C = b) DNE #Ø E = 8) Suppose we define a relation on the set {strings in A} by making 69°F a