# 4. Task and order of execution / Завдання та порядок виконання

> **Source of tasks.** Tasks 1–2 are taken **exactly** from the assignment
> *"Advanced Propositional Logic and Computational Logic"* (their input/output
> examples are authoritative). Tasks 3–4 **extend** the work to the level of its
> prerequisite, [Lecture 6](../../Lectures/CDM-L06.md) — implication/equivalence and a
> satisfiability/tautology decision.

## Order of execution

Implement in order and test each against its example; your score corresponds to the
highest band you complete correctly. Reuse the Task 1 evaluator throughout. *(The tables
below list `true` before `false`; Lecture 6 and Practical 3 instead list `false` first —
either order is acceptable as long as your program is consistent.)*

## Easy tasks (60–74 points)

### Task 1 — Complex logical expressions evaluation

Evaluate a logical expression, built from `AND`, `OR`, `NOT`, and parentheses,
under a given assignment of truth values to its variables.

- **Input:**
  - Expression: `"(A AND B) OR (NOT C)"`
  - Values: `{"A": true, "B": false, "C": true}`
- **Output:**
  - Result: `false`

### Task 2 — Automated truth table generation

Given a logical expression, generate its complete truth table — one row for every
combination of truth values of its variables.

- **Input:**
  - Expression: `"(A AND B) OR C"`
- **Output — Truth Table:**

| A | B | C | (A AND B) OR C |
|:--:|:--:|:--:|:--:|
| true | true | true | true |
| true | true | false | true |
| true | false | true | true |
| true | false | false | false |
| false | true | true | true |
| false | true | false | false |
| false | false | true | true |
| false | false | false | false |

## Medium tasks (75–89 points)

### Task 3 — Implication and equivalence
Extend the evaluator to the connectives `IMPLIES` ($\to$) and `IFF` ($\leftrightarrow$),
with precedence $\neg > \wedge > \vee > \to > \leftrightarrow$, and print the truth table
of the input expression.
- **Input:** Expression: `"(A IMPLIES B) IFF ((NOT B) IMPLIES (NOT A))"`
- **Output:** every row of the truth table is `true` — the expression is a **tautology**
  (it is the contrapositive law $A\to B \equiv \neg B\to\neg A$).

## Hard tasks (90–100 points)

### Task 4 — Satisfiability / tautology classifier
Given an expression, classify it by scanning its truth table as a **tautology** (true in
every row), a **contradiction** (false in every row), or a **contingency** (satisfiable
but not a tautology).
- **Input:** Expression: `"A AND (NOT A)"`
- **Output:** Classification: `Contradiction` (unsatisfiable).