Build the idea
Build exam-ready understanding by connecting the core idea, formulas or facts, worked example and previous NDA questions. Focus on why each rule works, then test it under timed conditions.
Concept
A set is a well-defined collection of distinct objects. Operations on sets (union ∪, intersection ∩, difference, complement) are visualised with Venn diagrams. A relation from set A to B is a subset of the Cartesian product A×B; a function is a special relation in which every element of A has exactly one image in B.
Key relation types are reflexive, symmetric, transitive; a relation that is all three is an equivalence relation.
Key Points & Formulas
- n(A∪B) = n(A) + n(B) − n(A∩B); for three sets add back n(A∩B∩C).
- De Morgan's laws: (A∪B)' = A'∩B' and (A∩B)' = A'∪B'.
- Cartesian product: if n(A)=m, n(B)=n, then n(A×B)=mn.
- A set with n elements has 2ⁿ subsets and 2ⁿ−1 proper subsets.
- Functions: one-one (injective), onto (surjective), bijective (both). Only bijective functions have an inverse.
Worked Example
Q. In a survey of 120 people, 70 read newspaper A, 55 read B and 25 read both. How many read at least one newspaper?
Use n(A∪B) = n(A)+n(B)−n(A∩B).
= 70 + 55 − 25 = 100.
So 100 people read at least one (and 120−100 = 20 read neither).