Set Notation: Union, Intersection & Complement
Grade 5The three key symbols
Set notation questions look intimidating until you know what three symbols mean:
A ∩ B — the intersection. This means "in A and B" — the overlap region only.
A ∪ B — the union. This means "in A or B (or both)" — everything inside either circle.
A′ — the complement. This means not in A — everything outside circle A, including the neither region.
Mapping symbols to regions
Every symbol maps directly to a shaded region of the Venn diagram. When you see a set notation expression, sketch the diagram and shade the region it describes — then count what's in the shading.
A ∩ B is just the lens. A ∪ B is the whole of both circles (the lens plus both side bits). A′ is everything outside circle A — right-hand bit of B plus the neither region.
Worked example
EXAMPLE
ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. A = {even numbers}. B = {multiples of 3}. Find (a) A ∩ B, (b) A ∪ B, (c) P(A′).
A = {2, 4, 6, 8, 10}. B = {3, 6, 9}.
(a) A ∩ B = numbers in both = {6}.
(b) A ∪ B = numbers in A or B or both = {2, 3, 4, 6, 8, 9, 10} — that's 7 numbers.
(c) A′ = numbers not in A = {1, 3, 5, 7, 9} — that's 5 numbers. P(A′) = 5/10 = 1/2.
Nested notation
Expressions like (A ∪ B)′ mean you find A ∪ B first, then take the complement. Work from the inside out — don't apply the ′ to each part separately.
