De Morgan's Laws

De Morgan's laws are two fundamental rules that relate AND, OR, and NOT operations. They are among the most important tools for simplifying Boolean expressions and converting between different gate types. The OCR H446 specification explicitly requires you to know and apply these laws.

---

The Two Laws

De Morgan's First Law: NOT(A AND B) = (NOT A) OR (NOT B)

De Morgan's Second Law: NOT(A OR B) = (NOT A) AND (NOT B)

In words:

• First law: The complement of a product (AND) is the sum (OR) of the complements.
• Second law: The complement of a sum (OR) is the product (AND) of the complements.

---

Intuitive Understanding

First Law — NOT(A AND B) = (NOT A) OR (NOT B): "It is not the case that both A and B are true" is the same as "either A is false, or B is false (or both)."

Second Law — NOT(A OR B) = (NOT A) AND (NOT B): "It is not the case that A or B is true" is the same as "A is false AND B is false."

---

Proving De Morgan's First Law with a Truth Table