Boolean Algebra Laws

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This lecture introduces Boolean Algebra Laws on a whiteboard, progressing from basic identities to De-Morgan's laws and set-theoretic interpretations. The instructor writes equations in maroon ink, beginning with the Idempotent Law (a.a = a and a+a = a), then Associative, Commutative, and Distributive laws. Set-form equivalents (A∩A=A, A∪A=A) are shown alongside algebraic forms. De-Morgan's laws (a+b̄ = ā·b̄ and ā.b̄ = ā + b̄) are introduced with a two-circle Venn diagram. The final section covers Identity, Complementation, and Involation laws with equations like a·1 = a and a+0 = a.

Chapters

1. 0:00 – 2:00 00:00-02:00

   The whiteboard header reads 'Boolean Algebra Laws' with a left-side list: Idempotent Law, Associative law, Commutative law, Distributive law. The instructor writes in maroon ink the equation 'a² = a x a' near the right side, followed by 'a⁰ = 1' and the rule 'a² = a a'. New handwritten lines appear reading '1² = 1' and a second line beginning with '1', establishing basic exponent rules before moving to Boolean identities.

2. 2:00 – 5:00 02:00-05:00

   The instructor presents the Idempotent Law with formulas 'a.a = a' and 'a+a = a', alongside set-form equivalents 'A∩A=A' and 'A U A = A' to the right of a vertical divider. He then works in the Associative law row, writing '(a.b).c = a.(b.c)' and below it '(a+b)+c = a+(b+c)'. A far-right column lists operator symbols including '+', '0', and union/empty-set marks, providing a reference for notation used throughout the lecture.

3. 5:00 – 10:00 05:00-10:00

   The board shows the Associative law section with '(a.b)c = a(b.c)' and '(a+b)+c = a+(b+c)', plus 'A∩B∩C = A∩(B∩C)' being written. Horizontal lines separate each law block as the instructor fills in 'a.b = b.a' and 'a+b = b+a' under Commutative law. The Distributive law appears as 'a.(b+c) = a.b + a.c'. The instructor then writes De-Morgan law by hand: 'a+b̄ = ā·b̄' and completes the second line as 'ā.b̄ = ā + b̄', adding a hand-drawn two-circle Venn diagram labeled 1, 2, 3 with region 4 outside to illustrate set relationships.

4. 10:00 – 12:02 10:00-12:02

   The board displays De-Morgan's law, Identity law, Complementation law, and Involation law. The instructor writes specific equations for each: 'a . 1 = a' and 'a + 0 = a' under Identity law. A Venn diagram with sets A and B is visible on the right, used to illustrate set operations corresponding to Boolean algebra identities. The lecture concludes with these additional laws completing the overview of fundamental Boolean Algebra properties.

The lecture systematically builds Boolean Algebra knowledge from simple exponent rules to complex identities. The teaching flow moves through four core laws (Idempotent, Associative, Commutative, Distributive) before introducing De-Morgan's laws and supplementary identities. Each algebraic law is paired with its set-theoretic equivalent, reinforcing the connection between Boolean algebra and set theory. The Venn diagram serves as a visual anchor for understanding how operations like intersection, union, and complementation map to AND, OR, and NOT. The notation column on the right provides a consistent reference for symbols used throughout.