Venn Diagrams

Shade and interpret two- and three-set Venn diagrams, reading and calculating cardinalities (n(A), n(A union B), n(A intersect B), n(A')), working backwards from a stated total to find a missing region, and combining Venn diagrams with basic algebra to find an unknown region.

Worksheet Builder All resources ☕ Shout us a flat white Download All

Te reo Māori terms

click each term to open in Te Aka

Learning objective overview

Master Teaching Guide coverage for this objective.

Current NZC (2007)
  • S4-4
New NZC (2026)
  • NZC26-P4-PRO-ETP-K-Y9-07
  • NZC26-P4-PRO-ETP-K-Y9-06
  • NZC26-P3-PRO-TP-K-Y7-05
  • NZC26-P3-PRO-TP-P-Y7-03

Resources

Terminology

  • Set
  • Universal set (Omega)
  • Union (union symbol)
  • Intersection (intersection symbol)
  • Complement (A')
  • Element
  • Cardinality, n(A)
  • Subset
  • Mutually exclusive sets
  • Venn diagram

Task goals

  • Read a region's value directly off a two- or three-set Venn diagram, and identify what a shaded region represents in words.
  • Calculate n(A), n(A union B), n(A intersect B), and n(A') (the complement) from a Venn diagram's regions.
  • Work backwards from a stated total and known regions to find one missing region.
  • Apply the inclusion-exclusion formula n(A union B) = n(A) + n(B) - n(A intersect B).
  • Read cardinalities from a three-set Venn diagram, including regions belonging to two or three sets at once.
  • Combine a Venn diagram with basic algebra to find an unknown region given the total, and identify the common error of adding the wrong two regions together.

Where this fits

What leads into this objective, and where it goes next.

Before

No prerequisite objective linked yet.

You are here

Venn Diagrams

Venn Diagrams

Know

Mutually exclusive events cannot occur together.

Statement▸
Year 9 · Probability · Experimental and theoretical probability
NZC26-P4-PRO-ETP-K-Y9-07

Next

The official curriculum has no separate Year 10 statements for Probability — Year 9 Probability spans the phase. Try the Statistics strand’s Year 10 statements.

Explore the whole sequence →