Chapter 1 · Class XI Mathematics · NCERT Exercises

Sets Exercises

From Venn Diagrams to De Morgan — Every NCERT Set Exercise Solved

📂 6 Exercise Files 📝 56 Questions 🎯 Foundation Level

▶ Start Exercise 1.1 📖 Revise Notes

Exercise Index

①

Exercise 1.1

Identifying sets; roster vs set-builder form

6 Q Easy

②

Exercise 1.2

Empty · finite · infinite · equal sets

6 Q Easy

③

Exercise 1.3

Subsets · power sets · universal set · intervals

9 Q Moderate

④

Exercise 1.4

Union · intersection · difference · Venn diagrams

12 Q Moderate

⑤

Exercise 1.5

Complement · De Morgan's Laws

7 Q Moderate

★

Miscellaneous

Mixed — n(A∪B) counting · word problems

16 Q Hard

6 exercise files · 56 total questions

Chapter Snapshot

JEE MainCBSE BoardsBITSAT

8Concepts

12Formulas

FoundationDifficulty

4–6%Weightage

Before You Begin

Prerequisites

✓Number systems (Class X)
✓Basic set notation ∈, ∉, ⊂
✓Venn diagram reading

Have Ready

🔧Plain paper for Venn diagrams
🔧NCERT Class XI textbook
🔧Notebook for proofs

Exercise-wise Topic Map

Exercise 1.1Recognise sets vs non-sets; roster and set-builder forms

Exercise 1.2Empty set ∅; finite vs infinite; equal sets check

Exercise 1.3All subsets; power set P(A); intervals as subsets of ℝ

Exercise 1.4A∪B, A∩B, A−B; Venn diagram shading; set identities

Exercise 1.5Complement A'; verify De Morgan's both sides

Miscellaneousn(A∪B∪C) survey problems; practical counting; proofs

Key Formulae — Recall Before Solving

\(n(A \cup B) = n(A)+n(B)-n(A \cap B)\)

\(n(A \cup B \cup C) = \Sigma n(A) - \Sigma n(A \cap B) + n(A \cap B \cap C)\)

\((A \cup B)' = A' \cap B'\ \mathrm{ (De\ Morgan\ 1)}\)

\((A \cap B)' = A' \cup B'\ \mathrm{ (De\ Morgan\ 2)}\)

\(|P(A)| = 2^{n(A)}\)

NCERT Solving Method

Step 1 — Identify which set operation is needed. Step 2 — Draw a Venn diagram for any 2+ set problem. Step 3 — For De Morgan proofs: simplify LHS and RHS independently — never assume the result. Step 4 — For counting word problems: assign n(A), n(B), n(A∩B) and apply the inclusion-exclusion formula.

Continue Your Preparation

📖 Notes Theory & concepts 🧠 MCQs Topic-wise practice 🎯 PYQs JEE · CBSE · BITSAT ⚖️ True–False Topic-wise concept check ➡️ Next Chapter Relations & Functions