make 5 question on sets with answers
Answers
1. Which of the following are well-defined sets?
(a) All the colors in the rainbow.
(b) All the points that lie on a straight line.
(c) All the honest members of the family.
(d) All the consonants of the English alphabet.
(e) All the tall boys of the school.
(f) All the efficient doctors of the hospital.
(g) All the hardworking teachers in a school.
(h) All the prime numbers less than 100.
(i) All the letters in the word GEOMETRY.
2. Let A = (a, b, c, d, e, f}. Insert the appropriate symbol ∈ or ∉ in the blank space.
(a) d __ A
(b) y __ A
(c) m __ A
(d) a __ A
(e) e __ A
(f) x __ A
3. Write the following sets in the set builder form.
(a) A = {2, 4, 6, 8}
(b) B = {3, 9, 27, 81}
(c) C = {1, 4, 9, 16, 25}
(d) D = {1, 3, 5, ......}
(e) E = {4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, ......., 52}
(f) F = {-10, ......, -3, -2, -1, 0, 1, 2, …..., 5}
(g) G = {O}
(h) P = { }
(i) H = {-5, 5}
(j) Q = {V, I, B, G, Y, 0, R}
4. Write the following sets in the roster form.
(a) A = {x : x ∈ W, x ≤ 5}
(b) B = {x : x ∈ I, -3 < x < 3)
(c) C = {x : x is divisible by 12}
(d) D = {x : x = 3p, p ∈ W, p ≤ 3}
(e) E = {x : x = a2, a ∈ N, 3 < a < 7}
(f) F = {x : x = n/(n + 1), n ∈ N and n ≤ 4}
(g) G = {x : x ∈ N, 3x - 2 < 5}
(h) J = {x : x ∈ N, x2 < 16}
(i) K = {x : x is a prime number which is a divisor of 42}
(j) H = {x : x is a 2-digit natural number such that the sum of its digits is 5}
5. Which of the following are the examples of an empty set?
(a) The set of even natural numbers divisible by 3.
(b) The set of all prime numbers divisible by 2.
(c) {x : x ∈ N, 5 < x < 6}
(d) The set of odd natural numbers divisible by 2.
(e) B = {O}
(f) C = { }
(g) D = {x : x ∈ R, x2 = -1}
(h) E = {x : x ∈ W, 3x + 1 = 2}
(i) P = {x : x is a prime number, 54 < x < 58}
(j) Q = {x : x = 2n + 3, n ∈ W, n ≤ 5}
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