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Samacheer Kalvi 9th Maths Solutions Chapter 1 Set Language Ex 1.2

Samacheer Kalvi 9th Maths Solutions Chapter 1 Set Language Ex 1.2

Samacheer Kalvi 9th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score full marks in your examinations.

Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 1 Set Language Ex 1.2

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 = {v : v =`\frac { 4 }{ 3n }` ,n ∈ N and 2 < n ≤ 5}

(iv) R = {x : x is an integers, 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) N = {1,2, 3, 4, …..}

n ∈ {3, 4, 5}

n(Q) = 3

(iv) x ∈ z

R = {-5, – 4, -3, -2, -1, 0, 1, 2, 3, 4}

n(R)= 10.

(v) S = {1884, 1888, 1892, 1896, 1904}

n (S) = 5.

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}

∴ Infinite set

(iv) x² – 5x + 6 = 0

(x – 3) (x – 2) = 0

B = {3, 2}

∴ 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 = A = { 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.

∴ Equivalent sets

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

D = {2, 3, 4}

∴ Unequal sets

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

Y = {F, I, L, E}

The sets X and Y contain the exactly the same elements.

∴ Equal sets.

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

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

∴ Equivalent sets.

Question 4.

Identify the following sets as null set or singleton set.

(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 in between 1 and 2 in Natural numbers.

∴ Null set

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

∴ B is Null set

(iii) C = {0}

∴ Singleton set

(iv) D = { }

∵ 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 = Ø, 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 radius.

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

(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 = Ø

Solution:

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

The power set of A

P(A ) = {Ø, {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

P(B) = {Ø, {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3}, {1, 2, 3}}

(iii) The subset of D are Ø, {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 D

P(D) = {Ø, {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

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)] = 2n = 2⁴ = 16

(ii) n(A) = 0

n[P(A)] = 2⁰ = 1

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

n[P(A)] = 28

∴ n(A) = 8.

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