The Empty Set
A set which does not contain any element is called the empty set or the null set or the void set.
EX.1.2
1. Which of the following are examples of the null set
(i) Set of odd natural numbers divisible by 2 - NULL SET
(ii) Set of even prime numbers - NOT A NULL SET
(iii) { x : x is a natural numbers, x < 5 and x > 7 } - NULL SET
(iv) { y : y is a point common to any two parallel lines}- NULL SET
FINITE AND INFINITE SETS:
A set which is empty or consists of a definite number of elements is called finite otherwise, the set
is called infinite.
2. Which of the following sets are finite or infinite
(i) The set of months of a year - FINITE
(ii) {1, 2, 3, . . .} - INFINITE
(iii) {1, 2, 3, . . .99, 100} - FINITE
(iv) The set of positive integers greater than 100 - INFINITE
(v) The set of prime numbers less than 99 - FINITE
3. State whether each of the following set is finite or infinite:
(i) The set of lines which are parallel to the x-axis- INFINITE
(ii) The set of letters in the English alphabet- FINITE
(iii) The set of numbers which are multiple of 5 - INFINITE
(iv) The set of animals living on the earth - FINITE
(v) The set of circles passing through the origin (0,0) – INFINITE
EQUAL SETS
Two sets A and B are said to be equal if they have exactly the same elements and we write A = B.
Otherwise, the sets are said to be unequal and we write A ≠ B.
4. In the following, state whether A = B or not:
(i) A = { a, b, c, d } B = { d, c, b, a } - A=B
(ii) A = { 4, 8, 12, 16 } B = { 8, 4, 16, 18 - A≠B
(iii) A = {2, 4, 6, 8, 10} B = { x : x is positive even integer and x ≤ 10} - A=B
(iv) A = { x : x is a multiple of 10}, B = { 10, 15, 20, 25, 30, . . . } - A≠B
