problem archive
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Write the set $\{ x : x \text{ is a positive integer and } x^2 < 40 \}$ in the roster form. -
Write the set A = {1, 4, 9, 16, 25, ...} in set-builder form. -
Write the set {1/2, 2/3, 3/4, 4/5, 5/6, 6/7} in the set-builder form. -
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... -
Which of the following are sets? Justify your answer. (i) The collection of all the months of a year beginning with the letter J. (ii) The collection ... -
Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank spaces: (i) 5 . . A (ii) 8 . . A (iii) 0 . . A (iv) 4 . . A (v) 2 . . A ... -
Write the following sets in roster form: (i) A = {x : x is an integer and -3 ≤ x < 7} (ii) B = {x : x is a natural number less than 6} (iii) C = {x : ... -
Write the following sets in the set-builder form: (i) {3, 6, 9, 12} (ii) {2, 4, 8, 16, 32} (iii) {5, 25, 125, 625} (iv) {2, 4, 6, ...} (v) {1, 4, 9, .... -
List all the elements of the following sets: (i) A = {x : x is an odd natural number} (ii) B = {x : x is an integer, 1/2 < x < 7/2} (iii) C = {x : x i... -
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 pr... -
State which of the following sets are finite or infinite: (i) {x : x ∈ N and (x - 1)(x - 2) = 0} (ii) {x : x ∈ N and x² = 4} (iii) {x : x ∈ N and 2x -... -
Given two sets A and B, if every element of A is also an element of B and if every element of B is also an element of A, then the sets A and B are sai... -
Find the pairs of equal sets, if any, give reasons: A = {0}, B = {x : x > 15 and x < 5}, C = {x : x - 5 = 0}, D = {x : x^2 = 25}, E = {x : x is an int... -
Which of the following pairs of sets are equal? Justify your answer. (i) X, the set of letters in “ALLOY” and B, the set of letters in “LOYAL”. (ii) A... -
Which of the following are examples of the null set (i) Set of odd natural numbers divisible by 2 (ii) Set of even prime numbers (iii) {x : x is a nat... -
Which of the following sets are finite or infinite (i) The set of months of a year (ii) {1, 2, 3, . . .} (iii) {1, 2, 3, . . .99, 100} (iv) The set of... -
State whether each of the following set is finite or infinite: (i) The set of lines which are parallel to the x-axis (ii) The set of letters in the En... -
In the following, state whether A = B or not: (i) A = {a, b, c, d}, B = {d, c, b, a} (ii) A = {4, 8, 12, 16}, B = {8, 4, 16, 18} (iii) A = {2, 4, 6, 8... -
Are the following pair of sets equal? Give reasons. (i) A = {2, 3}, B = {x : x is solution of x² + 5x + 6 = 0} (ii) A = {x : x is a letter in the word... -
From the sets given below, select equal sets: A = {2, 4, 8, 12}, B = {1, 2, 3, 4}, C = {4, 8, 12, 14}, D = {3, 1, 4, 2}, E = {-1, 1}, F = {0, a}, G = ...