Exercise 1. Which of the following are sets? Justify your answer.
- (i) The collection of all boys in your class.
- (ii) The collection of all even integers.
- (iii) The collection of nine most talented writers of India.
- (iv) A team of eleven best-cricket batsmen of the world.
- (v) A collection of novels written by the writer Rabindranath Tagore.
- (vi) The collection of all natural numbers less than 100.
- (vii) The collection of questions in this Chapter.
- (viii) The collection of all the months of a year beginning with the letter F.
- (ix) A collection of most dangerous animals of the world.
Exercise 2. Write the following sets in roster form:
- (i) F = The set of all letters in the word BETTER
- (ii) E = The set of all letters in the word TRIGONOMETRY
- (iii) B = {x : x is a natural number less than 6}
- (iv) D = {x : x is a prime number which is divisor of 60}
- (v) A = {x : x is an integer and –3 ≤ x < 7}
- (vi) C = {x : x is a two-digit natural number such that the sum of its digits is 8}
Exercise 3. Write the following sets in the set-builder form:
- (i) {2, 4, 6, . . .}
- (ii) {3, 6, 9, 12}
- (iii) {1, 4, 9, . . ., 100}
- (iv) {2, 4, 8,16, 32}
- (v) {5, 25, 125, 625}
Exercise 4. List all the elements of the following sets:
- (i) A = {x : x is an odd natural number}
- (ii) A = {x : x is an even natural number}
- (iii) B = {x : x is an integer, –1/2 < x < 11/2}
- (iv) C = {x : x is an integer, x2 ≤ 9}
- (v) D = {x : x is a letter in the word LOYAL}
- (vi) E = {x : x is a month of a year not having 31 days}
- (vii) F = {x : x is a consonant in the English alphabet which precedes k}
Exercise 5. Match each of the set on the left in the roster form with the same set on the right described in set-builder form:
(i) {1, 2, 3, 6} | (a) {x : x is a prime number and a divisor of 6} |
(ii) {M, A, T, H, E, I, C, S} | (b) {x : x is natural number and divisor of 6} |
(iii) {1, 3, 5, 7, 9} | (c) {x : x is an odd natural number less than 10} |
(iv) {2, 3} | (d) {x : x is a letter of the word MATHEMATICS} |
Exercise 6. Match each of the set on the left described in the roster form with the same set on the right described in the set-builder form:
(i) {P, R, I, N, C, A, L} | (a) { x : x is a positive integer and is a divisor of 18} |
(ii) {M, A, T, H, E, I, C, S} | (b) { x : x is an integer and x2 – 9 = 0} |
(iii) { 0 } | (d) {x : x is a letter of the word PRINCIPAL} |
(iv) {1, 2, 3, 6, 9, 18} | (c) {x : x is an integer and x + 1 = 1} |
Exercise 7. State True or False for the following statements.
- (a) If A is any set, then A ⊂ A.
- (b) Given that M = {1, 2, 3, 4, 5, 6, 7, 8, 9} and if B = {1, 2, 3, 4, 5, 6, 7, 8, 9}, then B ⊄ M.
- (c) The sets {1, 2, 3, 4} and {3, 4, 5, 6} are equal.
- (d) Q È Z = Q, where Q is the set of rational numbers and Z is the set of integers.
- (e) Let sets R and T be defined as R = {x Î Z | x is divisible by 2} and T = {x Î Z | x is divisible by 6}. Then T ⊂ R.
- (f) Given A = {0, 1, 2}, B = {x Î R | 0 ≤ x ≤ 2}. Then A = B.
There’s definately a great deal to know about this topic. I love all the points you made.