SET006 · Sets, relations & logic · Classes 9–11
Universal set
The universal set U contains every element under discussion. All other sets are subsets of U; it is drawn as the rectangle around a Venn diagram.
UUniversal set
📐 Formula
A ⊆ U for every set A; A′ = U − A
✏️ Worked example
U = {1, …, 12}, A = multiples of 2: everything outside A in U is A′ = {1, 3, 5, 7, 9, 11}.
🌍 Where it is used
Setting the context: all students of a school, all digits 0–9.
❓ Quick check
U is drawn in a Venn diagram as…
🏋️ Practice
EasyU = {1, …, 10}, A = {1, 2, 3}. A′ = ?
Answer: {4, 5, 6, 7, 8, 9, 10}
MediumWhat is U′?
Answer: ∅
ChallengeSuggest U for the sets of vowels and consonants.
Answer: The 26 letters of the alphabet