7.01a-c Existence problems, set notation and the pigeonhole principle Quiz: OCR Further Maths, Unit 4

The 20 questions

1. How many people must be in a room to guarantee at least two share a birth month?

   • 366
   • 13
   • 12
   • 24

2. Which mathematical symbol represents the power set, containing all subsets of a set A?

   • A'
   • P(A)
   • A x A
   • |A|

3. If a set A contains 4 elements, how many elements are in its power set P(A)?

   • 16
   • 24
   • 4
   • 8

4. Which set operation creates a set containing all elements that belong to set A, set B, or both?

   • Intersection
   • Set difference
   • Union
   • Cartesian product

5. What is the cardinality of the empty set, denoted by the symbol ∅?

   • Infinite
   • Undefined
   • 1
   • 0

6. Which standard mathematical symbol denotes that an element x belongs to set A?

   • x ∈ A
   • x ⊆ A
   • x ⊂ A
   • x = A

7. If set A has 3 elements and set B has 5 elements, what is |A x B|?

   • 125
   • 15
   • 8
   • 24

8. What term describes two sets whose intersection is equal to the empty set?

   • Complementary
   • Finite
   • Disjoint
   • Subset

9. Placing 10 items into 3 boxes guarantees at least one box contains at least how many items?

   • 4
   • 3
   • 5
   • 10

10. Which description correctly defines the set difference A \ B?

    • Union of both sets
    • Elements in both sets
    • Elements in A not B
    • Elements in B not A

11. If |A| = 10, |B| = 15, and |A ∩ B| = 4, what is |A ∪ B|?

    • 19
    • 21
    • 29
    • 25

12. What type of proof establishes that a mathematical object exists without explicitly constructing it?

    • Proof by induction
    • Non-constructive proof
    • Constructive proof
    • Direct proof

13. How many socks must be picked from 5 red and 5 blue socks to guarantee a matching pair?

    • 6
    • 11
    • 2
    • 3

14. What term describes a set of non-empty disjoint subsets whose union equals the original set?

    • Partition
    • Power set
    • Complement
    • Universal set

15. Which term refers to the set that contains all possible elements under consideration in a problem?

    • Universal set
    • Subset
    • Power set
    • Empty set

16. How many integers must be selected from {1, 2, ..., 10} to guarantee two sum to 11?

    • 10
    • 5
    • 7
    • 6

17. In set theory, what is the complement of the universal set U?

    • Subset
    • Power set
    • Universal set
    • Empty set

18. If set A is a proper subset of set B, which statement must be true?

    • A ∩ B = B
    • A ∪ B = A
    • A ∩ B = A
    • A \ B = A

19. How many people are needed to guarantee at least three share the same day of the week?

    • 15
    • 14
    • 8
    • 21

20. Which set operation represents elements that are in set A or set B, but not both?

    • Symmetric difference
    • Set intersection
    • Relative complement
    • Cartesian product

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