Skip to main content
Next exam on November 14 – 15, 2026:
All concepts

Sets and Set Operations

集合及其运算

Membership of an element in a set, inclusion (subset) relations between sets, and intersection, union and complement with their laws, operating on sets given by roster, description or interval/number-line form.

10 real-exam questions · 5 sittings41 in mock papers28 practice

Formulas

  • De Morgan's Laws

    Law
    ∁U(A∪B)=(∁UA)∩(∁UB),∁U(A∩B)=(∁UA)∪(∁UB)\complement_U(A\cup B)=(\complement_U A)\cap(\complement_U B),\quad \complement_U(A\cap B)=(\complement_U A)\cup(\complement_U B)

    Applies when：A and B are subsets of the universal set U

How the real exam tests it

Questions from real CSCA papers that test this concept. Work each one out before you open the answer.

  1. CSCA Math December 2025 Past Paper
    If A={1,2}A=\{1,2\} and B={1,2,3}B=\{1,2,3\}, then ( ).
    • A．B⊆AB \subseteq A
    • B．A∈BA \in B
    • C．A⊆BA \subseteq B
    • D．A=BA=B
    Show answer & solution

    Answer: C

    Answer: C All elements of AA are contained in BB, so A⊆BA\subseteq B. Choose C.
    See it in the full CSCA Math December 2025 Past Paper
  2. CSCA Math January 2026 Past Paper
    Let A={6,7,8,9,10}A=\{6,7,8,9,10\} and let ∅\varnothing denote the empty set. Which statement is correct?
    • A．9∈A9\in A
    • B．{6}∈A\{6\}\in A
    • C．6⊆A6\subseteq A
    • D．∅∈A\varnothing\in A
    Show answer & solution

    Answer: A

    Answer: A The elements of A={6,7,8,9,10}A=\{6,7,8,9,10\} are numbers. Thus 9∈A9\in A is true. The object {6}\{6\} is a set, not the number 6 itself, so {6}∉A\{6\}\notin A. The number 6 is not a set, so 6⊆A6\subseteq A is not valid. The empty set ∅\varnothing is not listed as an element of AA. Therefore only A is correct.
    Take the full CSCA Math January 2026 Past Paper — timed & graded
  3. CSCA Math March 2026 Past Paper
    Let M={x∣−5≤x<2}M = \{ x \mid - 5 \leq x < 2 \} and N={x∣−4≤x≤2}N = \{ x \mid - 4 \leq x \leq 2 \}. Then M∩N=M \cap N =
    • A．[−4,2)[ - 4,2 )
    • B．(−5,2)( - 5,2 )
    • C．[−5,2][ - 5,2 ]
    • D．(−4,2)( - 4,2 )
    Show answer & solution

    Answer: A

    The intersection takes the common part: M gives −5≤x<2- 5 \leq x < 2, N gives −4≤x≤2- 4 \leq x \leq 2. The overlap is −4≤x<2- 4 \leq x < 2, i.e., [-4, 2).
    Take the full CSCA Math March 2026 Past Paper — timed & graded

Real-exam evidence

Recorded past-paper appearances are listed below; online verification is labelled separately.

10 questions across 5 sittings1 of 5 sittings available to verify free online

41 questions across 16 mock papers — our own papers, so a coverage signal rather than real-exam evidence

28 related practice questions availablePractise free: Set

Sitting evidence comes from the CSCA past papers on record; questions whose original paper is missing are excluded, and sprint papers are deliberately not counted.

Glossary

setintersectionunioncomplement