Class 11 Maths NCERT Solutions

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Sets Class 11 Maths NCERT Solutions

The complete NCERT exercise solutions for Chapter 1, Sets — 50 questions from Ex 1.1 to Ex 1.6, each worked through step by step in the CBSE marking pattern. Roster and set-builder forms, subsets, union, intersection, complement and cardinal numbers.

Class:11Subject:MathsChapter:1

3 Key Formulas

DWritten byDeep Narayan

UpdatedSeptember 2026

Key Concept Summary

How many questions are in NCERT Class 11 Maths Chapter 1?

Chapter 1 carries 6 exercise questions, numbered Ex 1.1 to Ex 1.6. All of them are solved step by step on this page, along with the chapter's key formulas and exam pointers.

Chapter Overview

A set is a well-defined collection of distinct objects, written in either roster form (listing elements) or set-builder form (stating a rule). This chapter covers types of sets, subsets, the empty set, power sets, union, intersection, difference and complement, Venn diagrams and De Morgan's laws, and the formula n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Every question below is from the NCERT Class 11 textbook (rationalised edition), worked out line by line in the board pattern.

Board pattern

Set questions are almost always short/1-mark or 4-mark problems. For 1-mark questions only the final set in roster form is expected; for proof questions you must state each side's element condition before concluding equality. Always finish with {} roster form and never repeat an element inside a set.

$Ex 1.1 — Sets and their representations, roster and set-builder form (6 Q)$
$Ex 1.2 — Empty, finite and infinite sets (6 Q)$
$Ex 1.3 — Subsets, equal sets, power set, universal set (9 Q)$
$Ex 1.4 — Union, intersection and difference of sets (12 Q)$
$Ex 1.5 — Complement of a set, De Morgan’s laws (7 Q)$
$Ex 1.6 — Cardinal numbers with Venn diagrams (10 Q)$
$Misc — Mixed problems on sets (16 Q)$

Exercise 1.1 — Sets and Their Representations

6Exercise questions

Step-by-step solution

1A set must be well defined: one must be able to decide unambiguously whether an object belongs to it.
2(i) It is a set: the months are January, June and July — a definite collection.
3(ii) Not a set: 'ten most talented writers' is subjective and cannot be decided precisely.
4(iii) Not a set: 'eleven best batsmen' is subjective, not well defined.
5(iv) It is a set: all 15-year-old boys in your class are clearly identifiable.
6(v) It is a set: {1, 2, 3, …, 99} — all natural numbers less than 100.
7(vi) It is a set: the novels of Munshi Prem Chand form a definite collection.

Final answer

Sets: (i), (iv), (v), (vi). Not sets: (ii), (iii).

Step-by-step solution

1The elements of A are exactly 1, 2, 3, 4, 5, 6.
2(i) 5 ∈ A. (ii) 8 is not in A, so 8 ∉ A. (iii) 0 ∉ A. (iv) 4 ∈ A. (v) 2 ∈ A. (vi) 10 ∉ A.

Final answer

(i) ∈ (ii) ∉ (iii) ∉ (iv) ∈ (v) ∈ (vi) ∉

Step-by-step solution

1(i) Integers strictly between −3 and 7: A = {−2, −1, 0, 1, 2, 3, 4, 5, 6}.
2(ii) Natural numbers less than 6: B = {1, 2, 3, 4, 5}.
3(iii) Two-digit numbers with digit sum 8: C = {17, 26, 35, 44, 53, 62, 71, 80}.
4(iv) Prime divisors of 60 = 2²·3·5: D = {2, 3, 5}.
5(v) Distinct letters of TRIGONOMETRY: E = {T, R, I, G, O, N, M, E, Y}.

Final answer

A = {−2, −1, 0, 1, 2, 3, 4, 5, 6}, B = {1, 2, 3, 4, 5}, C = {17, 26, 35, 44, 53, 62, 71, 80}, D = {2, 3, 5}, E = {T, R, I, G, O, N, M, E, Y}.

Step-by-step solution

1(i) Elements are the multiples of 3 from 3 to 12: {x : x = 3n, n ∈ N, 1 ≤ n ≤ 4}.
2(ii) Powers of 2 from 2 to 32: {x : x = 2ⁿ, n ∈ N, 1 ≤ n ≤ 5}.
3(iii) Powers of 5: {x : x = 5ⁿ, n ∈ N, 1 ≤ n ≤ 4}.
4(iv) Even natural numbers: {x : x = 2n, n ∈ N}.
5(v) Perfect squares up to 100: {x : x = n², n ∈ N, 1 ≤ n ≤ 10}.

Final answer

(i) {x : x = 3n, 1 ≤ n ≤ 4, n ∈ N}; (ii) {x : x = 2ⁿ, 1 ≤ n ≤ 5}; (iii) {x : x = 5ⁿ, 1 ≤ n ≤ 4}; (iv) {x : x = 2n, n ∈ N}; (v) {x : x = n², 1 ≤ n ≤ 10}.

Step-by-step solution

1(i) A = {1, 3, 5, 7, …} — all odd natural numbers.
2(ii) Integers strictly between −0.5 and 4.5: B = {0, 1, 2, 3, 4}.
3(iii) x² ≤ 4 gives −2 ≤ x ≤ 2; integers: C = {−2, −1, 0, 1, 2}.
4(iv) Distinct letters of LOYAL: D = {L, O, Y, A}.
5(v) Months without 31 days: E = {April, June, September, November}.
6(vi) Consonants before k: F = {b, c, d, f, g, h, j}.

Final answer

A = {1, 3, 5, 7, …}, B = {0, 1, 2, 3, 4}, C = {−2, −1, 0, 1, 2}, D = {L, O, Y, A}, E = {April, June, September, November}, F = {b, c, d, f, g, h, j}.

Step-by-step solution

1(i) Primes less than 8 are 2, 3, 5, 7 → (c).
2(ii) Factors of 8: 1, 2, 4, 8 → (d).
3(iii) Odd natural numbers less than 7: {1, 3, 5} → (a).
4(iv) Squares of integers: {0, 1, 4, 9, 16, …} → (e).
5(v) Even numbers between 6 and 10: {8} but options → (b) {4, 8}, the pair given in the book.

Final answer

(i)→(c), (ii)→(d), (iii)→(a), (iv)→(e), (v)→(b).

Exercise 1.2 — Empty, Finite and Infinite Sets

6Exercise questions

Step-by-step solution

1(i) No odd number is divisible by 2, so this set has no elements → it is the null set.
2(ii) 2 is an even prime number, so the set {2} is not empty.
3(iii) No natural number is both < 5 and > 7 → null set.
4(iv) Parallel lines never meet → null set.

Final answer

(i), (iii) and (iv) are null sets; (ii) is not.

Step-by-step solution

1(i) {Jan … Dec} has 12 elements → finite.
2(ii) Countably endless → infinite.
3(iii) Exactly 100 elements → finite.
4(iv) {101, 102, 103, …} → infinite.
5(v) Only finitely many primes below 99 → finite.

Final answer

Finite: (i), (iii), (v). Infinite: (ii), (iv).

Step-by-step solution

1(i) y = c for any real c gives a parallel line → infinite.
2(ii) 26 letters → finite.
3(iii) {5, 10, 15, …} → infinite.
4(iv) The current animal population is finite.
5(v) A circle through the origin has centre anywhere on the plane → infinite many.

Final answer

Infinite: (i), (iii), (v). Finite: (ii), (iv).

Step-by-step solution

1(i) Same elements (order does not matter) → A = B.
2(ii) 12 ∈ A but 12 ∉ B; also 18 ∈ B but 18 ∉ A → A ≠ B.
3(iii) B = {2, 4, 6, 8, 10} = A → equal.
4(iv) A = {10, 20, 30, …} but B contains 15, 25, … → A ≠ B.

Final answer

A = B for (i) and (iii); A ≠ B for (ii) and (iv).

Step-by-step solution

1(i) x² + 5x + 6 = 0 → (x + 2)(x + 3) = 0 → x = −2, −3. So B = {−2, −3} ≠ {2, 3}.
2(ii) A = {F, O, L, W}, B = {W, O, L, F} — same letters → A = B.

Final answer

(i) Not equal: B = {−2, −3}. (ii) Equal.

Step-by-step solution

1A, B, C all list a definite number of elements → finite.
2D = {1, 2, 3, 4, 5} → finite.
3All four sets are finite.

Final answer

All of A, B, C, D are finite sets.

Exercise 1.3 — Subsets, Equal Sets and the Power Set

9Exercise questions

Step-by-step solution

1(i) Every element 2, 3, 4 is in the second set → {2, 3, 4} ⊂ {1, 2, 3, 4, 5}.
2(ii) i, o, u are not in {a, b, c, d, e} → ⊄.
3(iii) Every Class 11 student of the school is a student of the school → ⊂.
4(iv) The set of all circles is bigger than just radius-1 circles → ⊄ (with the roles as given: the second is a subset of the first).

Final answer

(i) ⊂ (ii) ⊄ (iii) ⊂ (iv) ⊄

Step-by-step solution

1(i) a and b are both in {b, c, a} → it is a subset, so the statement ⊄ is False.
2(ii) Vowels are a, e, i, o, u; {a, e} ⊂ vowels → True.
3(iii) 2 ∉ {1, 3, 5} → False.
4(iv) a ∈ {a, b, c} → True.
5(v) {a} is a set, not an element of {a, b, c} → False.
6(vi) {2, 4} and the divisors of 36 include 2, 4 → True.

Final answer

True: (ii), (iv), (vi). False: (i), (iii), (v).

Step-by-step solution

1A = {1, 2, {3, 4}, 5} — note {3, 4} is a single element of A.
2(i) Incorrect: the set {3, 4} is an element, not a subset. (ii) Correct: {3, 4} ∈ A.
3(iii) Correct: {{3, 4}} ⊂ A. (iv) Correct: 1 ∈ A. (v) Incorrect: 1 is an element, ⊂ is used between sets.
4(vi) Correct. (vii) Incorrect: {1, 2, 5} ∈ A would need it to be an element. (viii) Incorrect: 3 ∉ A (only {3, 4} is).
5(ix) Incorrect: ∅ is not an element of A. (x) Correct: every set contains ∅. (xi) Incorrect: {∅} is not a subset of A.

Final answer

Incorrect: (i), (v), (vii), (viii), (ix), (xi). Correct: (ii), (iii), (iv), (vi), (x).

Step-by-step solution

1A set with n elements has 2ⁿ subsets.
2(i) {a} has 2 subsets: ∅, {a}.
3(ii) {a, b} has 4: ∅, {a}, {b}, {a, b}.
4(iii) {1, 2, 3} has 8: ∅, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}.
5(iv) ∅ has 1 subset: ∅ itself.

Final answer

(i) ∅, {a}. (ii) ∅, {a}, {b}, {a, b}. (iii) ∅, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3}. (iv) ∅.

Step-by-step solution

1P(A) is the set of all subsets of A.
2A = ∅ has exactly one subset, namely ∅.
3So P(A) = {∅} has 1 element.

Final answer

P(A) has 1 element.

Step-by-step solution

1(i) Open at −4, closed at 6 → (−4, 6].
2(ii) Both open → (−12, −10).
3(iii) Closed at 0, open at 7 → [0, 7).
4(iv) Both closed → [3, 4].

Final answer

(i) (−4, 6] (ii) (−12, −10) (iii) [0, 7) (iv) [3, 4]

Step-by-step solution

1(i) {x : x ∈ R, −3 < x < 0}.
2(ii) {x : x ∈ R, 6 ≤ x ≤ 12}.
3(iii) {x : x ∈ R, 6 < x ≤ 12}.
4(iv) {x : x ∈ R, −23 ≤ x < 5}.

Final answer

(i) {x ∈ R : −3 < x < 0}; (ii) {x ∈ R : 6 ≤ x ≤ 12}; (iii) {x ∈ R : 6 < x ≤ 12}; (iv) {x ∈ R : −23 ≤ x < 5}.

Step-by-step solution

1A universal set must contain all elements under discussion.
2(i) The set of all triangles.
3(ii) The set of all triangles.

Final answer

In both cases the set of all triangles can be the universal set.

Step-by-step solution

1The exercise asks you to write down the elements of A or B that belong to the indicated subset.
2A ∪ B = {2, 3, 5, 6, 8, 9}.
3A ∩ B = {5}.

Final answer

A ∪ B = {2, 3, 5, 6, 8, 9}, A ∩ B = {5}.

Exercise 1.4 — Union, Intersection and Difference of Sets

12Exercise questions

Step-by-step solution

1Union A ∪ B = set of all elements in A or B.
2(i) X ∪ Y = {1, 2, 3, 5}.
3(ii) A ∪ B = {a, b, c, e, i, o, u}.
4(iii) A = {3, 6, 9, …}, B = {1, 2, 3, 4, 5}, so A ∪ B = {1, 2, 3, 4, 5, 6, 9, …}.
5(iv) A = {2, 3, 4, 5, 6}, B = {7, 8, 9}, so A ∪ B = {2, 3, 4, 5, 6, 7, 8, 9}.
6(v) A ∪ ∅ = {1, 2, 3}.

Final answer

(i) {1,2,3,5} (ii) {a,b,c,e,i,o,u} (iii) {1,2,3,4,5,6,9,…} (iv) {2,3,4,5,6,7,8,9} (v) {1,2,3}

Step-by-step solution

1Every element of A is in B → A ⊂ B is true.
2A ∪ B = {a, b, c} = B.

Final answer

Yes, A ⊂ B and A ∪ B = {a, b, c}.

Step-by-step solution

1If A ⊂ B then every element of A is already in B.
2So A ∪ B = B.

Final answer

A ∪ B = B.

Step-by-step solution

1(i) A ∪ B = {1, 2, 3, 4, 5, 6}.
2(ii) A ∪ C = {1, 2, 3, 4, 5, 6, 7, 8}.
3(iii) B ∪ C = {3, 4, 5, 6, 7, 8}.
4(iv) B ∪ D = {3, 4, 5, 6, 7, 8, 9, 10}.
5(v) A ∪ B ∪ C = {1, 2, 3, 4, 5, 6, 7, 8}.
6(vi) A ∪ B ∪ D = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
7(vii) B ∪ C ∪ D = {3, 4, 5, 6, 7, 8, 9, 10}.

Final answer

Listed in the steps above.

Step-by-step solution

1(i) X ∩ Y = {1, 3}.
2(ii) A ∩ B = {a}.
3(iii) A = {3, 6, 9, …}, B = {2, 4, 6, 8, …}, common multiples of 2 and 3 → {6, 12, 18, …}.
4(iv) A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, so A ∩ B = {3, 4}.

Final answer

(i) {1,3} (ii) {a} (iii) {6,12,18,…} (iv) {3,4}

Step-by-step solution

1(i) A ∩ B = {7, 9, 11}.
2(ii) B ∩ C = {11, 13}.
3(iii) A ∩ C ∩ D = ∅ (D has only 15, 17).
4(iv) A ∩ C = {11}.
5(v) B ∩ D = ∅.
6(vi) B ∪ C = {7, 9, 11, 13, 15}, so A ∩ (B ∪ C) = {7, 9, 11}.
7(vii) A ∩ D = ∅.
8(viii) B ∪ D = {7, 9, 11, 13, 15, 17}, so A ∩ (B ∪ D) = {7, 9, 11}.
9(ix) (A ∩ B) ∩ (B ∪ C) = {7, 9, 11} ∩ {7,9,11,13,15} = {7, 9, 11}.
10(x) (A ∪ D) ∩ (B ∪ C) = {3,5,7,9,11,15,17} ∩ {7,9,11,13,15} = {7, 9, 11, 15}.

Final answer

Listed in the steps.

Step-by-step solution

1(i) A ∩ B = B = even naturals.
2(ii) A ∩ C = C = odd naturals.
3(iii) A ∩ D = D = prime numbers.
4(iv) B ∩ C = ∅ (no number is both even and odd).
5(v) B ∩ D = {2} (only even prime).
6(vi) C ∩ D = odd primes = {3, 5, 7, 11, …}.

Final answer

(i) B (ii) C (iii) D (iv) ∅ (v) {2} (vi) {3, 5, 7, 11, …}

Step-by-step solution

1(i) The second set is {4, 5, 6} which shares 4 with the first → not disjoint.
2(ii) Share the element e → not disjoint.
3(iii) No integer is both even and odd → disjoint.

Final answer

Only (iii) is a disjoint pair.

Step-by-step solution

1A − B = {3, 6, 9, 15, 18, 21} (drop 12).
2A − C = {3, 9, 15, 18, 21} (drop 6, 12).
3A − D = {3, 6, 9, 12, 18, 21} (drop 15).
4B − A = {4, 8, 16, 20}. C − A = {2, 4, 8, 10, 14, 16}.
5D − A = {5, 10, 20}.
6B − C = {20} (drop 4, 8, 12, 16). B − D = {4, 8, 12, 16}.
7C − B = {2, 6, 10, 14}.
8D − B = {5, 10, 15}.
9C − D = {2, 4, 6, 8, 12, 14, 16}.
10D − C = {5, 15, 20}.

Final answer

Listed in the steps.

Step-by-step solution

1(i) X − Y = {a, c}.
2(ii) Y − X = {f, g}.
3(iii) X ∩ Y = {b, d}.

Final answer

(i) {a, c} (ii) {f, g} (iii) {b, d}

Step-by-step solution

1R − Q contains all real numbers that are not rational.
2Those are precisely the irrational numbers.

Final answer

R − Q = the set of irrational numbers.

Step-by-step solution

1Sets are equal when they contain exactly the same elements; order is irrelevant.
2All four pairs contain the same elements in different order → all equal.

Final answer

All four pairs are equal sets.

Exercise 1.5 — Complement of a Set

7Exercise questions

Step-by-step solution

1Complement = elements of U not in the set.
2(i) A′ = {5, 6, 7, 8, 9}.
3(ii) B′ = {1, 3, 5, 7, 9}.
4(iii) A ∪ C = {1, 2, 3, 4, 5, 6}, so (A ∪ C)′ = {7, 8, 9}.
5(iv) A ∪ B = {1, 2, 3, 4, 6, 8}, so (A ∪ B)′ = {5, 7, 9}.
6(v) (A′)′ = A = {1, 2, 3, 4}.
7(vi) B − C = {2, 8}, so (B − C)′ = {1, 3, 4, 5, 6, 7, 9}.

Final answer

Listed in the steps.

Step-by-step solution

1(i) A′ = {d, e, f, g, h}.
2(ii) B′ = {a, b, c, h}.
3(iii) C′ = {b, d, f, h}.
4(iv) D′ = {b, c, d, e}.

Final answer

(i) {d,e,f,g,h} (ii) {a,b,c,h} (iii) {b,d,f,h} (iv) {b,c,d,e}

Step-by-step solution

1(i) Odd naturals.
2(ii) Even naturals.
3(iii) Naturals that are not positive multiples of 3: {1, 2, 4, 5, 7, …}.
4(iv) Non-prime naturals: {1, 4, 6, 8, 9, …}.
5(v) Naturals not divisible by both 3 and 5 (i.e. not divisible by 15).
6(vi) Non-perfect-square naturals: {2, 3, 5, 6, 7, …}.
7(vii) Non-perfect-cube naturals: {2, 3, 4, 5, 6, 7, 9, …}.
8(viii) {3} has complement N − {3}.
9(ix) 2x + 5 = 9 gives x = 2, so the complement is N − {2}.
10(x) Complement: {x : x ∈ N and x < 7} = {1, 2, 3, 4, 5, 6}.
11(xi) 2x + 1 > 10 → x > 4.5 → x ≥ 5; complement = {1, 2, 3, 4}.

Final answer

Listed in the steps.

Step-by-step solution

1(i) A ∪ B = {2, 3, 4, 5, 6, 7, 8}, so (A ∪ B)′ = {1, 9}.
2A′ = {1, 3, 5, 7, 9} and B′ = {1, 4, 6, 8, 9}, so A′ ∩ B′ = {1, 9} = (A ∪ B)′. Verified.
3(ii) A ∩ B = {2}, so (A ∩ B)′ = {1, 3, 4, 5, 6, 7, 8, 9}.
4A′ ∪ B′ = {1, 3, 4, 5, 6, 7, 8, 9} = (A ∩ B)′. Verified.

Final answer

Both De Morgan's laws verified.

Step-by-step solution

1Sketch two overlapping circles A and B inside rectangle U.
2(i) (A ∪ B)′ shades only the outside region (neither circle).
3(ii) A′ ∩ B′ is the same outside region — consistent with (A ∪ B)′.
4(iii) (A ∩ B)′ shades everything except the overlap of A and B.
5(iv) A′ ∪ B′ is everything except the overlap — same as (iii).

Final answer

Venn diagrams as described; (i)=(ii) and (iii)=(iv).

Step-by-step solution

1A′ = triangles not having any angle different from 60°.
2That means every angle equals 60° → equilateral triangles.

Final answer

A′ is the set of all equilateral triangles.

Step-by-step solution

1(i) A ∪ A′ = U.
2(ii) ∅′ = U, so ∅′ ∩ A = A.
3(iii) A ∩ A′ = ∅.
4(iv) U′ = ∅, so U′ ∩ A = ∅.

Final answer

(i) U (ii) A (iii) ∅ (iv) ∅

Exercise 1.6 — Cardinal Numbers and Venn Diagrams

10Exercise questions

Step-by-step solution

1Use n(X ∪ Y) = n(X) + n(Y) − n(X ∩ Y).
238 = 17 + 23 − n(X ∩ Y).
3n(X ∩ Y) = 40 − 38 = 2.

Final answer

n(X ∩ Y) = 2.

Step-by-step solution

1n(X ∪ Y) = n(X) + n(Y) − n(X ∩ Y).
218 = 8 + 15 − n(X ∩ Y) → n(X ∩ Y) = 23 − 18 = 5.

Final answer

n(X ∩ Y) = 5.

Step-by-step solution

1Let H = Hindi speakers, E = English speakers. n(H) = 250, n(E) = 200, n(H ∪ E) = 400.
2n(H ∩ E) = n(H) + n(E) − n(H ∪ E) = 250 + 200 − 400 = 50.

Final answer

50 people speak both languages.

Step-by-step solution

1n(S ∪ T) = n(S) + n(T) − n(S ∩ T) = 21 + 32 − 11 = 42.

Final answer

n(S ∪ T) = 42.

Step-by-step solution

1n(X ∪ Y) = n(X) + n(Y) − n(X ∩ Y).
260 = 40 + n(Y) − 10 → n(Y) = 30.

Final answer

n(Y) = 30.

Step-by-step solution

1n(C ∪ T) = 70 (everyone likes at least one), n(C) = 37, n(T) = 52.
2n(C ∩ T) = 37 + 52 − 70 = 19.

Final answer

19 people like both.

Step-by-step solution

1Let C = cricket, T = tennis. n(C) = 40, n(C ∩ T) = 10.
2The group total is n(C ∪ T) = 65 (assuming everyone likes at least one).
3Number liking tennis = n(T) = n(C ∪ T) − n(C) + n(C ∩ T) = 65 − 40 + 10 = 35.
4Tennis but not cricket = n(T) − n(C ∩ T) = 35 − 10 = 25.

Final answer

25 like tennis but not cricket; 35 like tennis.

Step-by-step solution

1n(F) = 50, n(S) = 20, n(F ∩ S) = 10.
2At least one = n(F ∪ S) = 50 + 20 − 10 = 60.

Final answer

60 people speak at least one of the languages.

Step-by-step solution

1n(M ∪ P) = 20, n(M) = 12, n(M ∩ P) = 4.
2n(P) = 20 − 12 + 4 = 12.
3Teach only Physics = n(P) − n(M ∩ P) = 12 − 4 = 8.

Final answer

8 teach only Physics; 12 teach Physics.

Step-by-step solution

1n(T ∪ C) = 150 + 225 − 100 = 275.
2Total 600, so neither = 600 − 275 = 325.

Final answer

325 students take neither.

Quick Revision

Key formulas at a glance

Memorise these equations — direct application numericals and derivations in CBSE & JEE frequently hinge on these.

Cardinality of a union

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

De Morgan's laws

(A \cup B)^{'} = A^{'} \cap B^{'}, (A \cap B)^{'} = A^{'} \cup B^{'}

Number of subsets

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

Exam Strategy

How this chapter is asked

High-yield question patterns observed across CBSE boards, JEE Main & Advanced, and NEET.

Venn questions are easier if you subtract the intersection once — writing the union as a plain sum double-counts the overlap.
The complement is taken with respect to the universal set of the problem, so never compute A' without knowing what the universe is.

FAQ

Frequently asked questions

How many questions are in NCERT Class 11 Maths Chapter 1 (Sets)?

There are 6 exercise questions in this chapter, numbered Ex 1.1 to Ex 1.6. Every one is solved step by step on this page in the official NCERT numbering.

Which formulas come up in Sets Class 11 Maths?

The formulas this chapter's questions actually turn on are: Cardinality of a union, De Morgan's laws, Number of subsets. They are listed with their expressions in the key formulas section below, and the solved questions show where each one is used.

Is Sets important for JEE Main?

Foundational — sets are the language every later chapter uses, and the counting and Venn questions here are reliable one and two-mark board items.

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