that a student cannot study simultaneously in both Classes X and XI. Thus, the set B contains no element at all. Definition A set which does not contain any element is called the empty set or the null set or the void set . According to this definition, B is an empty set while A is not an empty set.
The empty set is denoted by the symbol φ or { }. We give below a few examples of empty sets. Let A = { x : < x < , x is a natural number}. Then A is the empty set, because there is no natural number between and .
B = { x : x – = and x is rational number}. Then B is the empty set because the equation x – = is not satisfied by any rational value of x . (iii) C = { x : x is an even prime number greater than }.Then C is the empty set, because is the only even prime number. (iv) D = { x : x = , x is odd }.
Then D is the empty set, because the equation x = is not satisfied by any odd value of x . . Finite and Infinite Sets Let A = { , , , , }, B = { a, b, c, d, e, g } and C = { men living presently in different parts of the world} We observe that A contains elements and B contains elements. How many elements does C contain?
As it is, we do not know the number of elements in C, but it is some natural number which may be quite a big number. By number of elements of a set S, we mean the number of distinct elements of the set and we denote it by n (S). If n (S) is a natural number, then S is non-empty finite set. Consider the set of natural numbers.
We see that the number of