(a, b,c]. determine if each is an equivalence relation on {(a, a), (a, c), (b, b), (c, a), (c, c)} 7. ((a, a), (b, b), (c, e)) 6. ((a, a), (b, b), (b, c), (e, b) 9. 8. o using the equivalence relation ((a, a), (a, b), (b, a), (b, b), (c, c), (d, d)) a (a, b,c, d), find each equivalence class. 13. [d] 11. b 12. [c] 10. [a] a fortran program contains 10 variables, a through j, and the following equivalence statement: equivalence (a, b,,e), (f, b), (c, h). find each class. 17. л 15. [в] 16. e 14. [a] using the equivalence relation in example 7.47, find the equivalence class represented by: 21. aaa 20. aa 19. b 18. a using the relation has the same length as on the set of words over the alphabet (a, b,c), find the equivalenpe class with each representative. 25. be 24. ab 22. 23. a 26. find the set of equivalence classes formed by the congruence relation modulo 4 on the set of integers. find the partition of the set (a, b,c) induced by each equivalence relation. 28. ((a, a), (a, c), (b, b), (c, a), (c, e)) [(a, a), (b, b), (c, e) 27. a fortran program contains the variables a through j. find the partition of the set of variables induced by each equivalence statement. 29. equivalence (a, b,,e), (f,,h) 30. equivalence (a,,,e, h) find the equivalence relation corresponding to each partition of the set (a, b,c, d). 31. (lal, (b, c), ld} 32. [la, b), (e, d) the number of partitions of a set with size n is given by sin, r), where sin, r) denotes a stirling number of the second kind. compute the number of partitions of a set with the given size. 33. two 34. three 35. four 36. five