4. Task and order of execution / Завдання та порядок виконання
Source of tasks. The seven tasks below are taken from the assignment; Tasks 6–7 extend it with antisymmetry and partial orders. Implement the described behaviour — the input/output examples are authoritative. Task numbers follow the assignment, so within a difficulty band they are not always consecutive.
Order of execution
The tasks are grouped into three difficulty bands. Implement them in order and test each against its example; your score corresponds to the band of tasks you complete correctly.
Easy tasks (60–74 points)
Task 1 — Reflexivity Checker
Objective: Write a program that checks if a relation is reflexive on a set.
- Input: Set:
{1, 2, 3}; Relation:{(1, 1), (2, 2), (3, 3)} - Output: Is Reflexive:
True
Task 2 — Symmetry Identifier
Objective: Implement a program that identifies if a relation on a set is symmetric.
- Input: Relation:
{(1, 2), (2, 1), (3, 3)} - Output: Is Symmetric:
True
Task 3 — Transitivity Verifier
Objective: Create a program to verify the transitivity of a relation on a set.
- Input: Relation:
{(1, 2), (2, 3), (1, 3)} - Output: Is Transitive:
True
Medium tasks (75–89 points)
Task 4 — Equivalence Relation Checker
Objective: Create a program that checks if a relation on a set is an equivalence relation (reflexive, symmetric, and transitive).
- Input: Set:
{1, 2, 3}; Relation:{(1, 1), (2, 2), (3, 3), (1, 2), (2, 1), (2, 3), (3, 2), (1, 3), (3, 1)} - Output: Is Equivalence Relation:
True
Task 6 — Antisymmetry Checker
Objective: Implement a program that checks whether a relation on a set is antisymmetric (no two distinct elements are related both ways).
- Input: Relation:
{(1, 1), (1, 2), (2, 3)} - Output: Is Antisymmetric:
True
Hard tasks (90–100 points)
Task 5 — Inverse Relation Generator
Objective: Implement a program that generates the inverse of a given relation.
- Input: Relation:
{(1, 2), (3, 4), (5, 6)} - Output: Inverse Relation:
{(2, 1), (4, 3), (6, 5)}
Task 7 — Partial Order Checker
Objective: Check whether a relation on a set is a partial order (reflexive, antisymmetric, and transitive).
- Input: Set:
{1, 2, 3}; Relation:{(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} - Output: Is Partial Order:
True