[9 marks] Let = {1, 2, 3, 4} and = {, , }. (a) [3 marks] Which of the following are elements of ? Reasons are not needed. Place ticks or crosses next to each element as appropriate. (1, 1) (1, ) (, ) (1, ) (, 3) (3, ) (b) [3 marks] Let be a relation on {1, 2, 3, 4} given by = {(1, 1), (1, 2), (1, 3), (2, 3)}. Is the relation reflexive? Symmetric? Transitive? You do not need to provide reasons. Circle each appropriate answer. Reflexive: Yes or No. Symmetric Yes or No. Transitive: Yes or No. (c) [3 marks] Recall that a partition of a non-empty set {1, 2, 3, 4} are non-empty sets 1 , 2 , , such that i.) = when and ii.) 1 2 = {1, 2, 3, 4}. Why do the sets 1 = {1, 2}, 2 = {2, 3} and 3 = {4} not form a partition of {1, 2, 3, 4}? Make a single change to the set 2 so that the sets 1 , 2 and 3 do form a partition of {1, 2, 3, 4}. 2 = With the sets 1 and 3 given above, and the set 2 you have just defined, let be the relation on {1, 2, 3, 4} where precisely when , . How many equivalence classes does have