A Note All infinite sets cannot be described in the roster form. For example, the set of real numbers cannot be described in this form, because the elements of this set do not follow any particular pattern. Example State which of the following sets are finite or infinite : { x : x ∈ N and ( x – ) ( x – ) = } { x : x ∈ N and x = } (iii) { x : x ∈ N and x – = } (iv) { x : x ∈ N and x is prime} (v) { x : x ∈ N and x is odd} Solution Given set = { , }. Hence, it is finite.
Given set = { }. Hence, it is finite. (iii) Given set = φ . Hence, it is finite.
(iv) The given set is the set of all prime numbers and since set of prime numbers is infinite. Hence the given set is infinite (v) Since there are infinite number of odd numbers, hence, the given set is infinite. . Equal Sets 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 said to be equal.
Clearly, the two sets have exactly the same elements. Definition 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. We consider the following examples : Let A = { , , , } and B = { , , , }.
Then A = B. Let A be the set of prime numbers less than and P the set of prime factors of . Then A and P are equal, since , and are the only prime factors of and also these are less than . A Note A set does not change if one or