4. Sets and Venn Diagrams

Venn Diagram Shading Lab

Venn diagram intersection and union explorer. Click logic operations to shade specific sets (A ∩ B, A ∪ B, A', etc.) on overlapping circles.

Virtual Viewport
Set ASet BIntersection
Card A [n(A)]
12
Card B [n(B)]
10
Union [n(A∪B)]
18

Active Sliders

ACircle A Elements12qty
520

Elements belonging to Set A.

BCircle B Elements10qty
520

Elements belonging to Set B.

A∩BIntersection4qty
08

Elements common to both Set A and Set B.

Syllabus Objectives

  • Identify set notation: union (∪), intersection (∩), complement (')
  • Shade Venn diagrams representing complex operations
  • Determine cardinality of intersection sets.

Mathematical Equations

Inclusion-Exclusion
n(A \cup B) = n(A) + n(B) - n(A \cap B)
De Morgan's Law
(A \cup B)' = A' \cap B'

Inquiry Guide Sheet

1

Select 'Intersection (A ∩ B)' and note the shaded middle region.

2

Select 'A union B Complement ((A ∪ B)′)'. Observe that everything outside both circles is shaded.

3

Compare A ∩ B' with A \ B. Verify they shade identical regions.