What a set is, three ways to describe one, subsets, and the union, intersection and complement of sets, with the notation CSEC expects.
5 narrated scenes. Press play, listen and read along — the points appear as they are explained. Use ‹ Prev / Next › or the scene bar to jump to any scene.
Sets are the grammar of mathematics — one idea, one tidy symbol — and they turn up again in probability, algebra and the SBA.
Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.
Copy these into your notebook in your own words — that is how they stick.
Element ∈, not element ∉, cardinality n(A), finite/infinite, universal set ξ, empty set ∅, complement A′.
Words, listing {1, 2, 3}, set-builder {x : 0 < x < 4, x ∈ ℕ}.
< and > exclude the end value; ≤ and ≥ include it. Check the type of number (ℕ, ℤ …).
B ⊂ A. ∅ ⊂ A. n elements → 2ⁿ subsets; 2ⁿ − 1 proper.
A ∪ B: either or both. A ∩ B: both. Disjoint: A ∩ B = ∅.
A′ = ξ − A; n(A′) = n(ξ) − n(A).
Equal: same elements. Equivalent: same number of elements.
n(A ∪ B) = n(A) + n(B) − n(A ∩ B).
3 quick games on this lesson. Earn XP and badges as you play — your best score for each game is saved. Games are for practice and do not change your exam readiness. More games in the Mathematics Arcade.
8 items modelled on real CSEC Paper 1 questions. Choose one answer for each, then check. Aim for 80% or better. Work each item on paper first.
Write full answers, then reveal the mark scheme and tick the points you earned (18 marks in total). Show all your working — method marks count. Your answers are saved on this device.
Question 1 [10 marks]
ξ = {x : 1 ≤ x ≤ 12, x ∈ ℕ}, A = {x : x is a factor of 12} and B = {x : x is a multiple of 3}.
(a) List the elements of A and of B. [3]
(b) Write down (i) A ∩ B, (ii) A ∪ B. [3]
(c) Write down n(A′) and list the elements of A′. [2]
(d) Verify that n(A ∪ B) = n(A) + n(B) − n(A ∩ B). [2]
Question 2 [8 marks]
Let S = {p, q, r, s}.
(a) How many subsets does S have? Show your working. [2]
(b) List all the subsets of S that have exactly 3 elements. [2]
(c) Write the set C = {x : −2 ≤ x < 3, x ∈ ℤ} by listing its elements. [2]
(d) State, with a reason, whether {0} and ∅ are the same set. [2]
Find these in your own past-paper booklets for extra timed practice. Items above are written in the style of these papers; any adapted from a specific question say so.