Samacheer Kalvi 9th Maths Book Solutions Chapter 1 | Set Language Answers For Tamil Nadu Board

Samacheer Kalvi 9th Maths Book Solutions Chapter 1 – Set Language is available here. The Samacheer Kalvi 9th Maths book answers of Chapter 1, available at BYJU’S, contain step by step explanations designed by our mathematics experts. All these important questions are based on the new pattern prescribed by the Tamil Nadu board. Students can also get the solutions of other chapters on Samacheer Kalvi 9th Maths solutions. Students are advised to first solve these Samacheer Kalvi Class 9 Maths Book Chapter 1 Questions first and then to refer to the solutions to self analyse one’s performance and exam preparation levels.

Samacheer Kalvi Class 9 Maths Book Chapter 1 Solutions

Chapter 1 of the Samacheer Kalvi 9th maths guide will help the students to solve problems related to the set, set notation, a descriptive form of a set, types of sets, subsets, disjoint sets, operations on sets, the complement of a set, union and intersection of sets, Venn diagrams, properties of set operations, De Morgan’s Laws, application on the cardinality of sets.

Samacheer Kalvi 9th Maths Chapter 1: Set Language Book Exercise 1.1 Questions and Solutions

Question 1: Which of the following are sets?

(i) The collection of prime numbers up to 100.

(ii) The collection of rich people in India.

(iii) The collection of all rivers in India.

(iv) The collection of good Hockey players.

Solution:

(i) The collection of prime numbers up to 100.

The statement is well defined.

It contains 2, 3, 5, 7, ……….97.

So, it is a set.

(ii) The collection of rich people in India.

The statement is not well defined and hence, it is not a set.

(iii) The collection of all rivers in India.

The statement is well defined and hence, it is a set.

(iv) The collection of good Hockey players.

The statement is not well defined and hence, it is not a set.

Question 2: List the set of letters of the following words in Roster form.

(i) INDIA

(ii) PARALLELOGRAM

(iii) MISSISSIPPI

(iv) CZECHOSLOVAKIA

Solution:

(i) INDIA

A = {I, N, D, A}

(ii) PARALLELOGRAM

B = {P, A, R, L, E, O, G, M}

(iii) MISSISSIPPI

C = {M, I, S, P}

(iv) CZECHOSLOVAKIA

D = {C, Z, E, H, O, S, L, V, A, K, I}

Question 3: Consider the following sets A = {0, 3, 5, 8}, B = {2, 4, 6, 10} and C = {12, 14,18, 20}.

(a) State whether True or False:

(i) 18 ∈ C

(ii) 6 ∉ A

(iii) 14 ∉ C

(iv) 10 ∈ B

(b) Fill in the blanks:

(i) 3 ∈ ____

(ii) 14 ∈ _____

(iii) 18 ____ B

(iv) 4 _____ B

Solution:

(i) 18 ∈ C

18 is the element of set C and hence it is true.

(ii) 6 ∉ A

The set A does not contain the element 6 and hence it is true.

(iii) 14 ∉ C

14 is the element of set C and hence the statement is false.

(iv) 10 ∈ B

10 is the element of set B, hence the statement is true.

(b)

(i) 3 is the element of set A, so 3 ∈ A.

(ii) 14 is the element of set C, so 14 ∈ C.

(iii) 18 is the element of set C, so 18 ∈ C.

(iv) 4 is the element of set B, so 4 ∈ B.

Question 4: Represent the following sets in Roster form.

(i) A = The set of all even natural numbers less than 20.

(ii) B = {y : y = 1 / 2n, n ∈ N , n ≤ 5}

(iii) C = {x : x is perfect cube, 27 < x < 216}

(iv) D = {x : x ∈ Z, –5 < x ≤ 2}

Solution:

(i) A = The set of all even natural numbers less than 20.

A = {2, 4, 6, 8, 10, 12, 14, 16, 18}

(ii) B = {y : y = 1 / 2n, n ∈ N , n ≤ 5}

If n = 1, then y = 1 / 2

If n = 2, then y = 1 / 4

If n = 3, then y = 1 / 6

If n = 4, then y = 1 / 8

If n = 5, then y = 1 / 10

B = { 1 / 2, 1 / 4, 1 / 6, 1 / 8, 1 / 10 }

(iii) C = {x : x is perfect cube, 27 < x < 216}

27 = 3³, 216 = 6³

C = {4³, 5³}

C = {64, 125}

(iv) D = {x : x ∈ Z, –5 < x ≤ 2}

D = {-4, -3, -2, -1, 0, 1, 2}

Question 5: Represent the following sets in set builder form.

(i) B = The set of all Cricket players in India who scored double centuries in One Day Internationals.

(ii) C = {(1 / 2), (2 / 3), (3 / 4)} .

(iii) D = The set of all Tamil months in a year.

(iv) E = The set of odd Whole numbers less than 9.

Solution:

(i) B = The set of all Cricket players in India who scored double centuries in One Day Internationals.

B = {x : x is an Indian player who scored double centuries in One Day International}

(ii) C = {1 / 2, 2 / 3, 3 / 4, ……….}

The denominator is greater than the numerator by 1.

C = {x : x = n / (n + 1) where n ∈ N}

(iii) D = The set of all Tamil months in a year.

D = {x : x is the set of all Tamil months in a year.}

(iv) E = The set of odd Whole numbers less than 9.

E = {x: x is the set of odd Whole numbers less than 9}

Question 6: Represent the following sets in descriptive form.

(i) P = {January, June, July}

(ii) Q = {7,11,13,17,19,23,29}

(iii) R = {x : x ∈ N , x < 5}

(iv) S = {x : x is a consonant in English alphabets}

Solution:

(i) P = { January, June, July}

P = The set of English months starting with J

(ii) Q = {7, 11, 13, 17, 19, 23, 29}

Q = the set of prime numbers between 5 and 31.

(iii) R = {x : x ∈ N, x < 5}

R = The set of natural numbers less than 5.

(iv) S = {x : x is a consonant in English alphabets}

S = The set of consonants in English alphabets

Tamil Nadu Board 9th Maths Chapter 1: Set Language Book Exercise 1.2 Questions and Answers

Question 1: Find the cardinal number of the following sets.

(i) M = {p, q, r, s, t, u}

(ii) P = {x : x = 3n + 2, n ∈ W and x < 15}

(iii) Q = {y : y = 4 / 3n , n ∈ N and 2 < n ≤ 5}

(iv) R = {x : x is an integer, x ∈ Z and –5 ≤ x <5}

(v) S = The set of all leap years between 1882 and 1906.

Solution:

(i) n (M) = 6

(ii) W = {0, 1, 2, 3, ……. }

if n = 0, x = 3 (0) + 2 = 2

if n = 1, x = 3 (1) + 2 = 5

if n = 2, x = 3 (2) + 2 = 8

if n = 3, x = 3 (3) + 2 =11

if n = 4, x = 3 (4) + 2 = 14

∴ P = {2, 5, 8, 11, 14}

n (P) = 5

(iii) Q = {y : y = 4 / 3n , n ∈ N and 2 < n ≤ 5}

The values of n are 3, 4, 5.

By applying the above three values for n, the different values of y are obtained.

Hence n(Q) is 3.

(iv) R = {x : x is an integer, x ∈ Z and –5 ≤ x < 5}

The elements of R are R = {-5,-4, -3, -2, -1, 0, 1, 2, 3, 4}

n (R) = 10

(v) S = The set of all leap years between 1882 and 1906.

The leap years 1884, 1888, 1892, 1896, 1900, 1904.

Hence n(S) = 6.

Question 2: Identify the following sets as finite or infinite.

(i) X = The set of all districts in Tamilnadu.

(ii) Y = The set of all straight lines passing through a point.

(iii) A = { x : x ∈ Z and x < 5}

(iv) B = { x : x² – 5x + 6 = 0, x ∈ N}

Solution:

(i) Finite set

(ii) Infinite set

(iii) A = { ……. , -2, -1, 0, 1, 2, 3, 4}

∴ It is an infinite set

(iv) x² – 5x + 6 = 0

(x – 3) (x – 2) = 0

B = {3, 2}

∴ It is a finite set.

Question 3: Which of the following sets are equivalent or unequal or equal sets?

(i) A = The set of vowels in the English alphabets.

B = The set of all letters in the word “VOWEL”

(ii) C = {2, 3, 4, 5} D = { x : x ∈ W, 1 < x < 5}

(iii) X = { x : x is a letter in the word “LIFE”} Y = { F, I, L, E}

(iv) G = { x : x is a prime number and 3 < x < 23} H = { x : x is a divisor of 18}

Solution:

(i) A = {a, e, i, o, u}

B = {V, O,W, E, L}

The sets A and B contain the same number of elements.

∴ The two sets are equivalent sets.

(ii) C = {2, 3, 4, 5}

D = {2, 3, 4}

∴ The two sets are unequal sets

(iii) X = {L, I, F, E}

Y = {F, I, L, E}

The sets X and Y contain exactly the same elements.

∴ The two sets are equal sets.

(iv) G = {5, 7, 11, 13, 17, 19}

H = {1, 2, 3, 6, 9, 18}

∴ The two sets are equivalent sets.

Question 4: Identify the following sets as null sets or singleton sets.

(i) A = {x : x ∈ N , 1 < x < 2}

(ii) B = The set of all even natural numbers which are not divisible by 2

(iii) C = {0}.

(iv) D = The set of all triangles having four sides.

Solution:

(i) A = { } ∵ There is no element between 1 and 2 in the set of natural numbers.

∴ It is a null set

(ii) B = { } ∵ All even natural numbers are divisible by 2.

∴ B is a null set

(iii) C = {0} ∴ Singleton set (iv) D = { }

(iv) No triangle has four sides.

∴ D is a Null set.

Question 5: State which pairs of sets are disjoint or overlapping?

(i) A = {f, i, a, s} and B = {a, n, f, h, s}

(ii) C = {x : x is a prime number, x > 2} and D = {x : x is an even prime number}

(iii) E = {x : x is a factor of 24} and F={x : x is a multiple of 3, x < 30}

Solution:

(i) A = {f, i, a, s}

B = {a, n, f, h, s}

A ∩ B = {f, i, a, s} ∩ {a, n, f h, s} = {f, a, s}

Since A ∩ B ≠ φ , A and B are overlapping sets.

(ii) C = {3, 5, 7, 11, ……}

D = {2}

C ∩ D = {3, 5, 7, 11, …… } ∩ {2} = { }

Since C ∩ D = φ, C and D are disjoint sets.

(iii) E = {1, 2, 3, 4, 6, 8, 12, 24}

F = {3, 6, 9, 12, 15, 18, 21, 24, 27}

E ∩ F = {1, 2, 3, 4, 6, 8, 12, 24} ∩ {3, 6, 9, 12, 15, 18, 21, 24, 27}

= {3, 6, 12, 24}

Since E ∩ F ≠ φ, E and F are overlapping sets.

Question 6: If S = {square, rectangle, circle, rhombus, triangle}, list the elements of the following subset of S.

(i) The set of shapes which have 4 equal sides.

(ii) The set of shapes which have a radius.

(iii) The set of shapes in which the sum of all interior angles is 180^o.

(iv) The set of shapes which have 5 sides.

Solution:

(i) {Square, Rhombus}

(ii) {Circle}

(iii) {Triangle}

(iv) Null set.

Question 7: If A = {a, {a, b}}, write all the subsets of A.

Solution:

A = {a, {a, b}} subsets of A are { } {a}, {a, b}, {a, {a, b}}.

Question 8: Write down the power set of the following sets:

(i) A = {a, b}

(ii) B = {1, 2, 3}

(iii) D = {p, q, r, s}

(iv) E = ∅

Solution:

(i) The subsets of A are φ, {a}, {b}, {a, b}

The power set of A is P(A ) = {φ, {a}, {b}, {a,b}}

(ii) The subsets of B are φ, {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3}, {1, 2, 3}

The power set of B is P(B) = {φ, {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3}, {1, 2, 3}}

(iii) The subset of D are φ, {p}, {q}, {r}, {s}, {p, q}, {p, r}, {p, s}, {q, r}, {q, s}, {r, s},{p, q, r}, {q, r, s}, {p, r, s}, {p, q, s}, {p, q, r, s}}

The power set of Dis P(D) = {φ, {p}, {q}, {r}, {s}, {p, q}, {p, r}, {p, s}, {q, r}, {q, s}, {r, s}, {p, q, r}, {q, r, s}, {p, r, s}, {p, q, s}, {p, q, r, s}

(iv) The power set of E is P(E) = { }.

Question 9: Find the number of subsets and the number of proper subsets of the following sets.

(i) W = {red, blue, yellow}

(ii) X = { x² : x ∈ N , x² ≤ 100}.

Solution:

(i) Given W = {red, blue, yellow}

Then n (W) = 3

The number of subsets = n[P(W)] = 2³ = 8

The number of proper subsets = n[P(W)] – 1 = 2³ – 1 = 8 – 1 = 7

(ii) Given X = {1,2,3, }

X² = {1, 4, 9, 16, 25, 36, 49, 64, 81, 100}

n (X) = 10

The Number of subsets = n[P(X)] = 2¹⁰ = 1024

The Number of proper subsets = n[P(X)] – 1 = 2¹⁰ – 1 = 1024 – 1 = 1023.

Question 10:

(i) If n(A) = 4, find n[P(A)].

(ii) If n(A) = 0, find n[P(A)].

(iii) If n[P(A)] = 256, find n(A).

Solution:

(i) n(A) = 4

n [P(A)] = 2⁴ = 16

(ii) If n(A) = 0, find n [P(A)].

n [P(A)] = 2m = 2⁰ = 1

(iii) n [P(A)] = 256

2m = 256

2^m = 2⁸

m = 8

Samacheer Kalvi 9th Maths Chapter 1: Set Language Book Exercise 1.3 Questions and Solutions

Question 1: Using the given Venn diagram, write the elements of

(i) A

(ii) B

(iii) A ∪ B

(iv) A ∩ B

(v) A – B

(vi) B – A

(vii) A′

(viii) B′

(ix) U

Solution:

(i) A = {2, 4, 7, 8, 10}

(ii) B = {3, 4, 6, 7, 9, 11}

(iii) A ∪ B = {2, 3, 4, 6, 7, 8, 9, 10, 11}

(iv) A ∩ B = {4, 7}

(v) A – B = {2, 8, 10}

(vi) B – A = {3, 6, 9, 11}

(vii) A’ = {1, 3, 6, 9, 11, 12}

(viii) B’ = {1, 2, 8, 10, 12}

(ix) U = {1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12}.

Question 2: Find A ∪ B, A ∩ B, A – B and B – A for the following sets.

(i) A = {2, 6, 10, 14} and B = {2, 5, 14, 16}

(ii) A = {a, b, c, e, u} and B = {a, e, i, o, u}

(iii) A = {x : x ∈ N, x ≤ 10} and B = {x : x ∈ W, x < 6}

(iv) A = Set of all letters in the word “mathematics” and B = Set of all letters in the word “geometry”.

Solution:

(i) A = {2, 6, 10, 14} and B = {2, 5, 14, 16}

A ∪ B = {2, 6, 10, 14} ∪ {2, 5, 14, 16} = {2, 5, 6, 10, 14, 16}

A ∩ B = {2, 6, 10, 14} ∩ {2, 5, 14,16} = {2,14}

A – B = {2, 6, 10, 14} – {2, 5, 14, 16} = {6, 10}

B – A = {2, 5, 14,16} – {2, 6, 10, 14} = {5,16}

(ii) A = {a, b, c, e, u} and B = {a, e, i, o, u}

A ∪ B = {a, b, c, e, u) ∪ {a, e, i, o, u) = {a, b, c, e, i, o, u}

A ∩ B = {a, b, c, e, u} ∩ {a, e, i, o, u} {a, e, u}

A – B = {a, b, c, e, u) – {a, e, i, o, u) = {b, c}

B – A = {a, e, i, o, u} – {a, b, c, e, u} = {i, o}

(iii) x ∈ {1,2, 3, ……..} ; x ∈ {0,1,2, 3, 4, 5, ……..}

A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

B = {0, 1, 2, 3, 4, 5}

A ∪ B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} ∪ {0, 1, 2, 3, 4, 5} = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A ∩ B = {1,2, 3,4, 5, 6, 7, 8, 9, 10} ∩ {0, 1, 2, 3,4, 5} = {1, 2, 3, 4, 5}

A – B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} – {0, 1, 2, 3, 4, 5} = {6, 7, 8, 9, 10}

B – A = {0, 1, 2, 3, 4, 5} – {1, 2, 3,4, 5, 6, 7, 8, 9, 10} = {0}

(iv) A= {m, a, t, h, e, i, c, s), B = {g, e, o, m, t, r, y)

A ∪ B = {m ,a, t, h, e, i, c, s} ∪ {g, e, o, m, t, r, y} = {m, a, t, h, e, i, c, s, g, o, r, y)

A ∩ B = {m, a, t, h, e, i, c, 5} ∩ {g, e, o, m, t,r,y} = {m, t, e}

A – B = {m ,a, t, h, e, i, c, s} ∪ {g, e, o, m, t, r, y} = {a, h, i, c, s)

B – A = {m, a, t, h, e, i, c, 5} ∩ {g, e, o, m, t,r,y} = {g, o, r, y}

Question 3: If U = {a, b, c, d, e, f, g, h}, A = {b, d, f, h} and B = {a, d, e, h}, find the following sets.

(i) A′

(ii) B′

(iii) A′ ∪ B′

(iv) A′ ∩ B′

(v) (A ∪ B)′

(vi) (A ∩ B)′

(vii) (A′)′

(viii) (B′)′

Solution:

(i) A’ = U – A = {a, b, c, d,e, f, g, y} – {b, d, f, h} = {a, c, e, g}

(ii) B’ = U – B = {a, b, c, d, e, f, g, y) – {a, d, e, h] = {b, c, f, g}

(iii) A’ ∪ B’= {a, c, e, g} ∪ {b, c, f, g} = {a, b, c, e, f g}

(iv) A’ ∩ B’= {a, c, e, g} ∩ {b, c, f, g} = {c, g}

(v) (A ∪ B)’ = U – (A ∪ B) = {a, b ,c, d, e ,f , g, y) – {a, b, d, e, f, h} = {c, g}

(vi) (A ∩ B)’ = U – (A ∩B) = {a, b, c, d, e, f, g, y} – {d, h} = {a, b, c, e,f, g}

(vii) (A’)’ = U – A’ = {a, b, c, d, e, f, g, h} – {a, c, e, g} = {b, d, f, h)

(viii) (B’)’ = U – B’ = {a, b, c, d, e, f, g, h} – {b, c, f, g} = {a, d, e, h}

Question 4: Let U = {0, 1, 2, 3, 4, 5, 6, 7}, A = {1, 3, 5, 7} and B = {0, 2, 3, 5, 7}, find the following sets.

(i) A′

(ii) B′

(iii) A′ ∪ B′

(iv) A′ ∩ B′

(v) (A ∪ B)′

(vi) (A ∩ B)′

(vii) (A′)′

(viii) (B′)′

Solution:

(i) A’ = U – A = {0, 1 ,2, y, 4, 5, 6, 7} – {1, 3, 5, 7} = {0, 2, 4, 6}

(ii) B’ = U – B = {0, 1, 2, 3, 4, 5, 6 ,7} – {0, 2, 3, 5, 7} = {1, 4, 6}

(iii) A’ ∪ B’ = {0, 2, 4, 6} ∪ {1, 4, 6} = {0, 1, 2, 4, 6}

(iv) A’ ∩ B’ = {0, 2, 4, 6} ∩ {1, 4, 6} = {4, 6}

(v) (A ∪ B)’ = U – (A ∪ B) = {0, 1, 2, 3, 4, 5, 6, 7} – {0, 1, 2, 3, 5, 7} = {4, 6}

(vi) (A ∩ B)’ = U – (A ∩ B)= {0, 1, 2, 3, 4, 5, 6, 7} – {3,5,7} = {0, 1, 2, 4, 6}

(vii) (A’)’ = U – A’ = {0, 1, 2, 3, 4, 5, 6, 7} – {0, 2, 4, 6} = {1, 3, 5, 7}

(viii) (B’)’ = U – B’ = {0, 1, 2, 3, 4, 5, 6, 7} – {1, 4, 6} = {0, 2, 3, 5, 7}.

Question 5: Find the symmetric difference between the following sets.

(i) P = {2, 3, 5, 7, 11} and Q = {1, 3, 5, 11}

(ii) R = {l, m, n, o, p} and S = {j, l, n, q}

(iii) X = {5, 6, 7} and Y = {5, 7, 9, 10}

Solution:

(i) P = {2, 3, 5, 7, 11}

Q = {1, 3, 5, 11}

P – Q = {2, 3, 5, 7, 11} – {1, 3, 5, 11} = {2, 7}

Q – P = {1, 2, 3, 411} – {2, 3, 5, 7, 11} = {1}

P ∆ Q = (P – Q) ∪ (Q – P) = {2, 7} ∪ {1} = {1, 2, 7}

(ii) R = {l, m, n, o, p}

S = {j, l, n, q}

R – S = {l, m, n, o, p) – {j, l, n, q} = {m, o, p)

s – R = {j, l, y, q) – {l, m, n, o, p}= {j, q}

R ∆ S = (R – S) ∪ (S – R) = {m, o, p) ∪ {j, q} = {j, m, o, p, q)

(iii) X = {5, 6, 7}

Y = {5, 7, 9, 10}

X – Y = {5, 6, 7} – {5, 7, 9, 10} – {6}

Y – X = {5, 6, 9, 10} – {5, 6, 7} = {9, 10}

X ∆ Y = (X – Y) ∪ (Y – X)= {6} ∪ {9, 10} = {6, 9, 10}.

Question 6: Using the set symbols, write down the expressions for the shaded region in the following.

Solution:

(i) X – Y

(ii) (X ∪ Y)’

(iii) (X – Y) ∪ (X – Y)

Question 7: Let A and B be two overlapping sets and the universal set be U. Draw appropriate Venn diagram for each of the following,

(i) A ∪ B

(ii) A ∩ B

(iii) (A ∩ B)′

(iv) (B – A)′

(v) A′ ∪ B′

(vi) A′ ∩ B′

(vii) What do you observe from the Venn diagram (iii) and (v)?

Solution:

(vii) From the diagram (iii) and (v) we observe that (A ∩ B)’ = A’ ∪ B’.