# NCERT SOLUTIONS FOR CLASS 11 MATHS CHAPTER 1 | SETS EX 1.3 |

Question 1. Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces:

• (i) {2, 3, 4} …{1, 2, 3, 4, 5}
• (ii) {a, b, c}… {b, c, d}
• (iii) {x: x is a student of Class XI of your school} … {x: x student of your school}
• (iv) {x : x is a circle in the plane}… {x: x is a circle in the same plane with radius 1 unit}
• (v) {x : x is a triangle in a plane}… {x : x is a rectangle in the plane}
• (vi) {x: x is an equilateral triangle in a plane} … {x: x is a triangle in the same plane}
• (vii) {x: x is an even natural number}… {x: x is an integer}

Solution.

(i) {2, 3, 4} ⊂ {11, 2, 3, 4, 5}

(ii) [a, b, c) ⊄ {{b, c, d}

(iii) {x : x is a student of Class XI of your school} ⊂ {x : x student of your school}

(iv) {x : x is a circle in the plane} ⊄ {x : x is a circle in the same plane with radius 1 unit}

(v) {x : x is a triangle in a plane} ⊄ {x : x is a rectangle in the plane}

(vi) {x : x is an equilateral triangle in a plane} ⊂ {x : x is a triangle in the same plane}

(vii) {x: x is an even natural number} ⊂ {x: x is an integer}

Question 2. Examine whether the following statements are true or false:

• (i) {a, b} ⊄{b, c, a}
• (ii) {a, e} ⊂ {x : x is a vowel in the English alphabet}
• (iii) {1, 2, 3} ⊂ {1, 3, 5}
• (iv) {a} ⊂ {a, b, c}
• (v) {a} ∈ la, b, c}
• (vi) {x: x is an even natural number less than 6} ⊂ {x: x is a natural number which divides 36}

Solution.

Question 3. Let A = {1, 2, {3, 4}, 5}. Which of the following statements are incorrect and why?

Solution.

Question 4. Write down all the subsets of the following sets

• (i) {a}
• (ii) {a,b}
• (iii) {1,2,3}
• (iv) φ

Solution.

(i) Number of elements in given set = 1

Number of subsets of given set = 21 = 2

∴ Subsets of given set are φ , {a}.

(ii) Number of elements in given set = 2
Number of subsets of given set = 212 = 4
∴ Subsets of given set are φ, {a}, {b}, {a, b}.

(iii) Number of elements in given set = 3
Number of subsets of given set = 23 = 8
Subsets of given set are φ, {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3}, {1, 2, 3}.

(iv) Number of elements in given set = 0
Number of subsets of given set = 20= 1
∴ Subset of given set is φ.

Question 5. How many elements has P(A), if A = φ?

Solution.

Number of elements in set A = 0

Number of subset of set A = 20 = 1

Hence, number of elements of P(A) is 1.

Question 6. Write the following as intervals:

• (i) {x: x ∈ R, -4 < x ≤ 6}
• (ii) {x: x ∈ R, -12 < x < -10}
• (iii) {x: x ∈ R, 0 ≤ x < 7}
• (iv) {x: x ∈ R, 3 ≤ x ≤ 4}

Solution.

(i)Let A = {x: x ∈ R, -4 < x ≤ 6}

It can be written in the form of interval as (-4, 6)

(ii) Let A= {x: x ∈ R, -12 < x < -10}

It can be written in the form of interval as (-12, -10)

(iii) Let A = {x: x ∈ R, 0 ≤ x < 7}

It can be written in the form of interval as (0, 7).

(iv) Let A = {x: x ∈ R, 3 ≤ x ≤ 4}

It can be written in the form of interval as (3,4).

Question 7. Write the following intervals in set-builder form:

• (i) (-3,0)
• (ii) [6, 12]
• (iii) (6, 12]
• (iv) [-23, 5)

Solution.

(i) The interval (-3, 0) can be written in set-builder form as {x : x ∈ R,-3 < x < 0}.

(ii) The interval [6, 12] can be written in set-builder form as {x : x ∈ R, 6 ≤ x ≤ 12}.

(iii) The interval (6, 12] can be written in set-builder form as {x : x ∈ R, 6 < x ≤ 12}

(iv) The interval [-23,5) can be written in set-builder form as {x : x ∈ R, -23 ≤ x < 5}

Question 8. What universal set(s) would you propose for each of the following:

• (i) The set of right triangles.
• (ii) The set of isosceles triangles.

Solution.

(i) Right triangle is a type of triangle. So the set of triangles contain all types of triangles.

∴ U = {x : x is a triangle in a plane}

(ii) Isosceles triangle is a type of triangle. So the set of triangles contain all types of triangles.
∴ U = }x : x is a triangle in a plane}

Question 9.

Given the sets A = {1, 3, 5},

B = {2, 4, 6} and

C = {0, 2, 4, 6, 8},

which of the following may be considered as universal set(s) for all the three sets A, B and C

• (i) {0, 1, 2, 3, 4, 5, 6}
• (ii) φ
• (iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
• (iv) {1, 2, 3, 4, 5, 6, 7, 8}

Solution.

(i) {0, 1, 2, 3, 4, 5, 6} is not a universal set for A, B, C because 8 ∈ C but 8 is not a member of {0, 1, 2, 3, 4, 5, 6}.

(ii) φ is a set which contains no element. So it is not a universal set for A, B, C.

(iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is a universal set for A, B, C because all members of A, B, C are present in {0,1 , 2, 3, 4, 5, 6, 7, 8, 9, 10).

(iv) (1, 2, 3, 4, 5, 6, 7, 8) is not a universal set for A, B, C because 0 ∈ C but 0 is not a member of {1, 2, 3, 4, 5, 6, 7, 8)