1. Objective / Мета роботи #

Gain fluency with Boolean formulas — building a function’s truth table from its formula, and reducing formulas to disjunctive and conjunctive normal form by the laws of Boolean algebra.

By the end of the class the student should be able to:

• evaluate a Boolean formula on every interpretation of its variables and so construct its truth table, numbering the $2^n$ rows in the standard order and computing the value in each;
• apply operator precedence ($\neg > \wedge > \vee > \to > \leftrightarrow$) and the laws of Boolean algebra — double negation, De Morgan, distributivity, absorption, idempotence, the complement laws — to rewrite a formula while preserving its meaning;
• eliminate implications and equivalences in favour of $\neg,\wedge,\vee$, and push negations inward to the variables using De Morgan’s laws;
• reduce a formula to disjunctive normal form (DNF) — an OR of AND-terms — and to conjunctive normal form (CNF) — an AND of OR-clauses;
• recognise when a reduction collapses to a constant ($0$ for a contradiction, $1$ for a tautology).

The class consolidates Lecture 4 — Boolean algebra basics and the normal forms of Lecture 6 — Propositional logic. All theory needed is restated, self-contained, in 2method.md.

Practical/Practical3/1purpose.md · 1.4 KB · updated 2026-08-01 20:18