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

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## 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.**