(iii) A = {2, 4, 6, 8, 10} B = {x : x is a positive even integer and x < 10}
(iv) A = {x : x is a multiple of 10} B = {10, 15, 20, 25, 30, …}
4. State the reasons for the following :
(i) }1, 2, 3, …., 10} ≠ {x : x ∈ N and 1 < x < 10}
(ii) {2, 4, 6, 8, 10} ≠ {x : x = 2n+1 and x ∈ N}
(iii) {5, 15, 30, 45} ≠ {x : x is a multiple of 15}
(iv) {2, 3, 5, 7, 9} ≠ {x : x is a prime number}
5. List all the subsets of the following sets.
(i) B = {p, q} (ii) C = {x, y, z} (iii) D = {a, b, c, d}
(iv) E = {1, 4, 9, 16} (v) F = {10, 100, 1000}
2.8 FINITE AND INFINITE SETS
Now consider the following sets:
(i) A = {the students of your school} (ii) L = {p,q,r,s}
(iii) B = {x : x is an even number} (iv) J = {x : x is a multiple of 7}
Can you list the number of elements in each of the sets given above? In (i), the number of
elements will be the number of students in your school. In (ii), the number of elements in set L is
4. We find that it is possible to express the number of elements of sets A and L in definite whole
numbers. Such sets are called finite sets.
Now, consider the set B of all even numbers. We can not express the number of elements
in whole number i.e., we see that the number of elements of this set is not finite. We find that the
number of elements in B and J is infinite. Such sets are called infinite sets.
We can draw infinite number of straight lines passing though a given point. So this set is
infinite. Similarly, it is not possible to find out the last number among the collection of all integers.
Thus, we can say a set is infinite if it is not finite.
Consider some more examples :
(i) Let ‘W’ be the set of the days of the week. Then W is finite.