Q6-12 points Define functions  ​f​ , ​g​ , ​h​  from {1, 2,…

Q6-12 points Define functions  ​f​ , ​g​ , ​h​  from {1, 2, 3, 4} to {​a​, ​b​, ​c​, ​d​} as follows: f (1) = a,  f (2) = b, f (3) = a,  f (4) = b g(1) = a,  g(2) = d, g(3) = c,  g(4) = b h(1) = d,  h(2) = a, h(3) = a, h(4) = a                                                                                                    Which of these functions are well-defined? ​                                                                                                                                              Which of these functions are onto?                      Which of these functions are one-to-one?         

Q6-12 points Define functions  ​f​ , ​g​ , ​h​  from {1, 2,…

Q6-12 points Define functions  ​f​ , ​g​ , ​h​  from {1, 2, 3, 4} to {​a​, ​b​, ​c​, ​d​} as follows: f (1) = a,  f (2) = b, f (3) = c,  f (4) = d  g(1) = a,  g(2) = a, g(3) = b,  g(4) = b h(1) = d,  h(2) = a, h(3) = c, h(4) = b                                                                                                 Which of these functions are well-defined? ​                                                                                                                                              Which of these functions are onto?                      Which of these functions are one-to-one?         

Q4-12 points Let ​C ​= {2, 4, 8}, ​A​ = ​C ​×​ C​, and defin…

Q4-12 points Let ​C ​= {2, 4, 8}, ​A​ = ​C ​×​ C​, and define a relation on ​A​ by: (​u​, ​v​) ​R ​(​x​, ​y​) if and only if ​uv ​=​ xy​. Prove  that ​R​ is an equivalence relation on ​A​. Remember that the elements of ​A are ordered pairs. ​ Compute the partition ​A/R​ that corresponds to the equivalence relation. Hint: Keep in mind that you are partitioning the 9 elements of ​A ​into blocks. ​