Numerical: Write the set A = { 1, 4, 9, 16, 25,... } in set-builder form.
Solution: Number 1, 4, 6, 16, 25.. are squares of natural numbers 1,2, 3,4, 5 etc..
Therefore set ={ x: x is a square of N }
Empty or null or void set
Set which does not contain any element is called the empty set or the null set or the void set. The empty set is denoted by the symbol φ or { }.
Examples of empty sets. Let A = { x: 5 < x < 6, x is a natural number }. Then A is the empty set, Thus we dente A set by the symbol φ or { }.
Please note that A = { x: 5 < x < 6, x is a real number } is not empty set, as there are many real number between 5 & 6.
Finite & infinite set
A set which is empty or consists of a definite number of elements is called finite otherwise, the set is called infinite.
E. g. A = { 1, 2, 3, 4, 5 } Finite: n( A)= 5. B = { all natural numbers } n( S): number of distinct elements Examples of infinite & finite set:
In-finite: n( B)= infinite
1. Let W be the set of the days of the week. Then W is finite. 2. Let G be the set of points on a line. Then G is infinite. 3. Let A be set of rats in India, then A is infinite. 4. Let B be set of months in a year, then B is finite. 5. Let P be set of all prime numbers, the P is infinite.