Sets
Class 11 · Mathematics
4 ideas in Class 11 Mathematics, explained in plain words, with games and quizzes to practise.
Sets and Representations
Part of: Sets and Kinds
Well-defined collections with ∈ marks list by roster or describe by rule; N, Z, Q and R name number families while order and repetition never matter.
Why it matters. Precise membership tests every later definition. Two forms fit finite and infinite collections.
Formulas
- A = B means every element of A is in B and vice versa
Key words
- Set
- : A well-defined collection of distinct objects taken as a whole.
- Element
- : One object belonging to a set.
- Roster form
- : Writing a set by listing its members inside braces.
- Set-builder form
- : Writing a set by stating the rule its members follow.
- Equal sets
- : Two sets holding exactly the same members.
Try it in two minutes
- Test well-definedness.
- List by roster.
- Describe by rule.
Try at home. Sort home objects into sets.
Special Sets and Subsets
Part of: Sets and Kinds
Empty holds nothing, singletons hold one, finite ends while infinite runs on; equal shares elements, subsets nest, proper subsets leave members behind, and m elements beget two-to-m subsets.
Why it matters. Nesting tests unlock proofs. Power counts predict subset totals.
Formulas
- Subsets of an m-element set: 2^m
- Proper subsets of an m-element set: 2^m - 1
Key words
- Empty set
- : The set with no members, written as {} or phi.
- Singleton
- : A set holding exactly one member.
- Finite set
- : A set whose members can be counted to an end.
- Infinite set
- : A set whose members never run out.
- Subset
- : A set with every member also in another set.
- Proper subset
- : A subset that leaves at least one member of the parent out.
- Power set
- : The set of all subsets of a given set.
Try it in two minutes
- Spot empty versus singleton.
- Test subset both ways.
- Double subsets per element.
Try at home. List all subsets of {1, 2, 3}.
Venn Diagrams and Operations
Part of: Operations and Counting
Venn circles union, overlap, subtract and complement sets inside universal rectangles; De Morgan flips unions to intersections under complements while intersections distribute over unions.
Why it matters. Diagram logic visualises every law. Duality halves proof work.
Formulas
- De Morgan: complement of (A union B) = (complement of A) intersect (complement of B)
- De Morgan: complement of (A intersect B) = (complement of A) union (complement of B)
Key words
- Union
- : Members belonging to A or B or both.
- Intersection
- : Members belonging to both A and B.
- Difference
- : Members of A that are not in B.
- Complement
- : Members of the universal set that are not in A.
- Universal set
- : The big set inside which all sets under study live.
- Disjoint sets
- : Two sets with no member in common.
Try it in two minutes
- Shade union versus intersection.
- Complement inside rectangles.
- Flip with De Morgan.
Try at home. Draw Venn for two classes.
Counting with Venn Diagrams
Part of: Operations and Counting
Overlaps counted twice subtract once; triple overlaps add back; survey numbers split into only, both and neither regions.
Why it matters. Inclusion-exclusion prevents double counts. Region splits answer surveys.
Formulas
- n(A union B) = n(A) + n(B) - n(A intersect B)
- For three sets, add the triple overlap back at the end
Key words
- Venn diagram
- : A diagram of overlapping circles showing set relations.
- Overlapping region
- : The lens where two circles overlap, holding common members.
- Only-A region
- : Members belonging to A but not to B.
- Neither region
- : Members outside all circles, belonging to none of the sets.
Try it in two minutes
- Subtract the overlap.
- Split only, both, neither.
- Add back triple overlaps.
Try at home. Survey friends on two likes.
What your child will practise
- Counting with Venn Diagrams: Space Puzzle (Clue Puzzle)
- Counting with Venn Diagrams: Space Quick Fire (Quick Fire)
- Sets and Representations: Ocean Puzzle (Clue Puzzle)
- Special Sets and Subsets: Jungle Quest (Flip and Match)
- Venn Diagrams and Operations: Candy Quick Fire (Quick Fire)
- Quiz: Counting with Venn Diagrams (8 questions)
- Quiz: Sets and Representations (8 questions)
- Quiz: Special Sets and Subsets (8 questions)
- Quiz: Venn Diagrams and Operations (8 questions)