Students can practice TS 10th Class Maths Solutions Chapter 2 Sets Ex 2.3 to get the best methods of solving problems.
TS 10th Class Maths Solutions Chapter 2 Sets Exercise 2.3
Question 1.
Which of the following sets are equal ?
a) A = {x : x is a letter in the word FOLLOW’}
b) B = {x : x is a letter in the word ‘FLOW’}
c) C = {x : x is a letter in the word ‘WOLF’}
Answer:
a) Writing the given set in the roaster form, we have A = {F, O, L, W}
b) Writing the given set in the roaster form, we have B = {F, L, O, W}
c) Writing the given set in the roaster form, we have C = {W, O, L, F}
Therefore, A, B, C are equal sets.
[∴ The sets A, B, C have exactly the same elements]
Question 2.
Consider the following sets and fill up the blank in the statement given below with = or ≠ so as to make the statement true.
A = {1, 2, 3};
B = {The first three natural numbers}
C = {a, b, c, d};
D = {d, c, a, b}
E = {a, e, i, o, u};
F = {set of vowels in English Alphabet}
i) A ……… B
ii) A …….. E
iii) C ……. D
iv) D …… F
v) F ……. A
vi) D …… E
vii) F ……. B
Answer:
i) A = B
ii) A ≠ E
iii) C=D
iv) D ≠ F
v) F ≠ A
vii) D ≠ E
viii) F ≠ B
Question 3.
In each of the following, state whether
A = B or not.
i) A = {a, b, c, d}; B = {d, c, a, b}
ii) A = {4, 8, 12, 16}; B = {8, 4, 16, 18}
iii) A = (2, 4, 6, 8, 10)
B = {x: x is a positive even integer and x ≤ 10}
iv) A = {x: x ¡s a multiple of 10};
B = {10, 15, 20, 25, 30,……. }
Answer:
i) A = B because A and B have exactly the same elements i.e., a, b, c, d.
ii) A ≠ B because A and B have not exactly the same elements.
iii) A = B because A and B have exactly the same elements.
Writing B in roaster form, we have
B = {2, 4, 6, 8, 10}
iv) A = {10, 20, 30, 40,……..}
B = {10, 15, 20, 25,……..}
A ≠ B because A and B have not exactly the same elements.
Question 4.
State the reasons for the following:
i) {1,2, 3,…, 10} ≠ {x : x ∈ N and 1 < x < 10}
ii) {2, 4, 6, 8, 10} ≠ {x : x = 2n + 1 and x ∈ N}
iii) {5, 15, 30, 45} ≠ {x : x is a multiple of 15
iv) {2, 3, 5, 7, 9} ≠ {x : x is a prime number}
Solution:
The first set is {1, 2, 3, ……, 10}
Writing the second set in roaster form, we have {2, 3, 4, ……, 9}
The first set and the second set have not exactly the same elements.
∴ {1, 2, 3,……10} ≠ {x : x ∈ N and 1 < x < 10}
ii) The first set is {2, 4, 6, 8, 10}
Writing the second set in roaster form, we have {3, 5, 7, 9, ….}
∴ {2, 4, 6, 8, 10} ≠ {3, 5, 7, 9, ….}
x = 2n + 1 means x is odd.
iii) The first set is {5, 15, 30, 45}
Writing the second set in roaster form, we have {15, 30, 45, 60, …}
∴ {5, 15, 30, 45} ≠ {15, 30, 45, 60,…}
5 does not exist, since x is multiple of 15.
iv) The first set is {2, 3, 5, 7, 9}
Writing the second set in roaster form, we have {2, 3, 5, 7, 11, 13,…}
∴ {2, 3, 5, 7, 9} ≠ {2, 3, 5, 7, 11, 13 }
9 is not a prime number.
Question 5.
List all the subsets of the following sets.
i) B = {p, q}
ii) C = {x, y, z}
iii) D = {a, b, c, d}
iv) E = {1, 4, 9, 16}
v) F = {10, 100, 1000}
Solution:
i) {p}, {q}, {p, q}, { ϕ }
ii) {x}, {y}, {z}, {x, y}, {y, z}, {x, z}, {x, y, z}, {ϕ}
iii) {a}, {b}, {c}, {d}, {a, b}, {b, c}, {c, d}, {a, c}, [a, d}, {b, d}, {a, b, c}, {b, c, d}, {a, b, d}, {a, c, d}, {a, b, c, d}, {ϕ}
iv) {1}, {4}, {9}, {16}, {1, 4}, {4, 9}, {9, 16}, {1, 9}, {1, 16}, {4, 16}, {1, 4, 9}, {4, 9, 16}, {1, 4, 16}, {1, 9, 16}, {1, 4, 9, 16}, {ϕ}
v) {10}, {100}, {1000}, {10, 100}, {100, 1000}, {10, 1000}, {10, 100, 1000}, {ϕ}