Sets
Notation, subsets, the operations that combine sets and the Venn diagrams that count them.
Problems
- When a Nested Intersection Empties
- Integers in a Union of Intervals
- The Set of $3m-1$
- Divisible by 3 but Not by 2
- Multiples of 3 and of 5
- Element or Subset?
- Integers in Both Intervals
- Multiples of 2 and Multiples of 3
- Digits of a Page Group
- At Least Two, At Most Two
- Even Numbers Meet Multiples of 3
- Divisors of Two Numbers
- Three Parasites
- Leaving After Primary School
- Drums, Guitar and Violin
- Land, Water and Air
- A Set That Depends on p
- Sets Inside Sets
- Elements That Are Sets
- Squares Under Control
- Pages Without a 1 or a 2
- Girls, Boys and Two Sections
- Four Computer Games
- A Survey on Five Series
- Android or iOS
- Two Arithmetic Progressions
- Six Desserts
- One Progression Minus Another
- Ages in a Group
- When $B$ Comes From an Intersection
- From Pairs to Triples
- Equal Rings
- Two In, One Out
- No Digits Allowed
- At Least One Letter
- Nothing Is Left
- Subsets That Contain 4 or 5
- Sets Squeezed Between A and B
- Subsets of a Union
- Inside A, Containing A − B
- Subsets They Share
- Only Vowels
- Two or Three Elements
- Between {a, b} and {a, …, f}
- With a, Without c
- Subsets of the Overlap
- How Many Sets $C$?
- Caught Between Two Sets
- Five Elements, Three From the Front
- Counting the Possible $B$
- A Two-Digit Number of Subsets
- At Least Two From $B$
- A Prescribed Intersection
- Exactly One Vowel
- Missing $x$ or Missing $y$
- Strictly Above $X$
- Complement of a Ring
- Counting Proper Subsets
- Adding Up Every Subset
- At Least Thirteen
- Matching Subset Counts
- At Least Two Letters
- One Is In, $x$ or $y$ Is Out
- Three More Elements
- Two Subset Counts That Agree
- Three Claims About $x$ and $y$
- A Mean Above the Middle
- All Subsets Against the Pairs
- Five From Seven
- An Even Product
- Six Elements In Between
- The Missing Element
- A Mean Below Five
- Multiplying Every Subset
- Odd Sums of Three
- How Many Choices for B?
- Between A ∩ B and A ∪ B
- Odd Images of A
- Two More Elements
- At Least Six Elements
- Proper Subsets and the Union
- Subset Counts Adding to 49
- Every Subset of {1, 2, 3, 4}
- Negatives Come in Blocks
- Six and Its Divisors
- Pairs Sharing One Element
- Mysterious Sets
- Co-intersection Sets
- Element and Subset at Once
- Subsets and Proper Subsets
- Pairs Without a Prime
- Subsets Against Proper Subsets
- Small Subsets, Large Subsets
- A Difference of 4950
- None Inside Another
- With −2 but Without −4
- Sums of Subsets
- Recovering a Set from a Difference
- A Difference With One Element
- Adding Two Complement Equations
- De Morgan Inside $A$
- Two Sums, One Universe
- A Sum of Complements
- Recovering A − B
- Not Coprime to 10
- A Difference of a Difference
- From Bᶜ to (A ∩ B)ᶜ
- Elements in Exactly One Set
- Finding a and b
- (A ∩ B)ᶜ ∩ B
- Keeping Two Intervals Apart
- When the Union Is Smaller
- The Middle Set Alone
- Difference of Intervals
- Counting in a Three-Circle Diagram
- Two Unions, One Intersection
- Counting $B$ Inside a Small Universe
- Listing a Complement
- Three Counts, One Set
- Simplify the Expression
- Three Claims About Sets
- An Unknown in the Union
- Three Points on a Line
- Spot the Faulty Step
- Three Steps to the Universe
- Everything Collapses
- Digits, Even and Small
- Two Absolute Values
- Simplify It
- A Combination of Complements
- A Complement Swallows a Set
- How Big Can $B$ Be?
- An Expression That Vanishes
- A Union Through a Difference
- Name the Shaded Region
- Finding k from B − A
- A Square Hidden in A
- Sum of the Elements of B
- (B − A)ᶜ Rewritten
- Counting Aᶜ ∪ Bᶜ
- Simplify Before You Choose
- Recovering B
- Two Quadratics Sharing a Root
- Multiples of 4 Meet Multiples of 6
- Inside the Ring
- Intersection of Intervals
- Differences of Complements
- The Four-Digit Password
- Who Comes on Day 21?
- Three Relations, One Universe
- Pinning Down $A\cap C$
- Three Sets, Two Empty Overlaps
- Chained Ratios
- Complements on the Real Line
- A Chain of Three Sets
- Inclusion–Exclusion for Three Sets
- Reading a Venn Diagram
- Two Equations for One Union
- Three Equal Regions
- Billiards or Darts
- The Smallest Possible Union
- Counting B from the Outside
- Elements in Only One Set
- Outside the Overlap
- Counting A ∩ Bᶜ
- The Shaded Outside
- Bus and Subway
- The Largest Overlap
- Subsets of the Overlap Again
- Finding n(A − B)
- Difference from Complements
- Eyes and Glasses
- Only English in a Class of 34
- How Big Is the Group?
- Failing Exactly One
- Women Who Don't Speak English
- The Largest Two-Digit Union
- The Smallest $N$ That Fits
- The Part of $B$ Outside Everything
- Three Regions That Cannot Be Empty
- English, German, or Neither
- Only German, Only French
- Who Came With Both Parents?
- Basketball or Football
- Sea and Forest Paintings
- A Ratio and Two Differences
- Three Days a Week
- Three Differences and a Core
- Cables on a Street
- How Big Can $A$ Be?
- A Set Inside a Union
- How Wide Can the Union Be?
- Letters in a Name
- Fig and Pomegranate Trees
- Planes and Helicopters
- A Night at the Camp
- Pens in Three Colours
- Two Languages on a Plane
- Escalators and Lifts
- Belonging to Exactly One
- Two Conditions on B − A
- Three Regions in Proportion
- Largest and Smallest Overlap
- As Much of A as Possible
- Three Equal Ratios
- Counting Subsets of A − B
- Neither 5 nor 6
- Biggest and Smallest Union
- Multiples of 3 or 4
- A Inside B
- Complements Only
- Only Football
- Only English
- All Three versus None
- Passing Math or English
- Exactly One Subject
- Only French
- Exactly Two Sports
- A Day at the Appliance Store
- Three Kinds of Juice
- Guitar or Violin
- Three Languages on a Plane
- Smallest Plus Largest
- Soup, Meat and Vegetables
- Three Languages, Four Clues
- Players, Boys and Girls
- At Most How Many Know Neither?
- Course A or Course B
- The Smallest x
- Union from a Chain of Ratios
- The Largest Possible Class
- Fewest Who Play Nothing
- Fewest Who Play Both