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Venn diagrams reference

Set theory symbols and definitions

Use an original printable reference to set notation, unions, intersections, complements, subset relations and number sets, with clear definitions and examples.

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Read the symbol, its definition and the example together. State the universe when interpreting a complement.

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Definitions worth checking carefully

The reference distinguishes subset from proper subset, disjointness from not being a subset, and an element from a set containing it. Examples use an explicit universe for complements and state the convention for natural numbers.

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Learning objective

What this activity builds

Read common set notation and connect each symbol to a precise membership rule.

Worked example

If A = {1, 2} and B = {2, 3}, is A a subset of B?

No. The element 1 belongs to A but not to B.

The sets may overlap even when one is not a subset of the other. One missing element is enough to disprove the subset relation.

Teaching notes

Make the practice count

  • Distinguish an element from a set containing that element.
  • Use examples with overlap when teaching “not a subset”.
  • Check that a power set contains every subset, including the empty set.
  • State whether a course includes zero in its natural numbers.

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Math SheetNameScoreTeacherDateSet Theory Symbols ReferenceUse this reference to read and write set notation.{ }SetsA set is a well-defined collection of distinctobjects.A = {1, 2, 3}UnionContains everything in either set or both.A={1,2}; B={2,3}; {1,2,3}IntersectionContains everything common to the sets.A={1,2}; B={2,3}; {2}SubsetEvery element of the first set is in the second.{1,2}; {1,2,3}Proper subsetA subset that is not equal to the containing set.{1,2}; {1,2,3}Not a subsetAt least one element of the first set is absent fromthe second.{1,4}; {1,2,3}SupersetContains every element of the other set.{1,2,3}; {1,2}Proper supersetContains the other set and at least one extraelement.{1,2,3}; {1,2}Not a supersetMisses at least one element of the other set.{1,2}; {1,3}PPower setContains every subset, including the empty andwhole sets.P({a,b}) = {{ },{a},{b},{a,b}}Equal setsContain exactly the same elements.{1,2} = {2,1}AComplementElements of U outside the named set; also writtenU difference A.U={1,2,3}; A={1,2}; {3}math-sheet.comPage 1 / 2
Math SheetNameScoreTeacherDateSet Theory Symbols ReferenceUse this reference to read and write set notation.DifferenceElements in the first set but not the second.A={1,2}; B={2,3}; {1}Symmetric differenceElements in exactly one of the two sets.A={1,2}; B={2,3}; {1,3}MembershipThe object belongs to the set.2 ; {1,2,3}NonmembershipThe object does not belong to the set.4 ; {1,2,3}Empty setHas no elements.{ }UUniversal setContains every object under discussion.A ; UNPositive natural numbersUnder this convention, natural numbers begin atone.{1,2,3,...}NNatural numbers including zeroSome texts include zero; always state theconvention.{0,1,2,3,...}ZIntegersWhole numbers and their negatives.{...,-2,-1,0,1,2,...}QRational numbersRatios of integers with nonzero denominator.3/4RReal numbersAll points on the number line.sqrt(2)CComplex numbersNumbers a + bi, where i squared is -1.2 + 3imath-sheet.comPage 2 / 2

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