5. Which relation on the set {1, 2, 3, 4} is an equivalence relation and contain {(1, 2), (2, 3), (2, 4), (3, 1)}. 6. Find the transitive closures of the relation {(1, 1), (1,4), (2,1), (2,3), (3,1), (3, 2), (3,4), (4, 2)} on the set {1, 2, 3, 4}. 7. Let R be the relation on the set {1, 2, 3, 4, 5} containing the ordered pairs (1, 1), (1, 2), (1, 3), (2, 3), (2, 4), (3, 1), (3, 4), (3, 5), (4, 2), (4, 5), (5, 1), (5, 2), and (5, 4). Find a) R3 b) R4 8. Which of these relations on the set of all people are equivalence relations? Determine the properties of an equivalence relation that the others lack. a) {(a, b) | a and b are the same age} b) {(a, b) | a and b have the same parents} c) {(a, b) | a and b speak a common language}