Find the transitive closure of the relation R={(1,2),(2,2), (2,3),(3,3)} on the set A=(1,2,3}. Select one: O a. ={(2,2),(3,1).(2.2).(2,3).(3,3)}. O b. =((1,1).(3,1).(2.2).(2,3),(3,3)}. O c. ={(1,3),(3,1),(2,2),(2,3),(3,3)}. O d. ={(1,2),(1,3).(2,2).(2,3).(3,3)}. O e. =((1,2),(3,1), (2,2), (2,3),(3,3)}.

Specifically part d please

For (a,b),(c,d) E N×N define the relation (a,b) ~ (b,c) if and only if ab = cd. Is this relation symmetric and transitive? True False

Let ? = {1, 2, 3, 4, 5, 6, 7} and define a relation ? ⊆ ? × ? by? = {(1,1), (1,2), (1,3), (2,3), (7,1), (7,2), (7,3), (4,5), (4,6), (5,6), (5,5)}Determine (yes or no) whether ? has the following properties (no justification is required).