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 natural number, x < 5 and x > 7 }
(iv) { y : y is a point common to any two parallel lines }
(i), (iii), (iv)
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 positive integers greater than 100
(v) The set of prime numbers less than 99
(i) Finite (ii) Infinite (iii) Finite (iv) Infinite (v) Finite
State whether each of the following sets is finite or infinite:
(i) The set of lines which are parallel to the x-axis
(ii) The set of letters in the English alphabet
(iii) The set of numbers which are multiple of 5
(iv) The set of animals living on the earth
(v) The set of circles passing through the origin (0,0)
(i) Infinite (ii) Finite (iii) Infinite (iv) Finite (v) Infinite
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, 10}, B = {x : x is positive even integer and x ≤ 10}
(iv) A = {x : x is a multiple of 10}, B = {10, 15, 20, 25, 30, ...}
(i) Yes (ii) No (iii) Yes (iv) No
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 FOLLOW}, B = {y : y is a letter in the word WOLF}
(i) No (ii) Yes
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 = {1, −1}, H = {0, 1}
B = D, E = G