Loading....
Coupon Accepted Successfully!

 

Set Builder Form

We can also define a set by stating properties which its elements must satisfy. For example, let E denote the set of all even natural numbers, then we use a letter, usually x, to represent an arbitrary element and we write:
This is read as "E is the set x such that x is an even natural number." Note that the "/"  or ":" is read as "such that". This method of representing a set is called set builder form

Illustration
Let H be the set of all human beings on the earth, that is = {x / x is a human being on the earth}.

 

Illustration
Let l P be a fixed line in the plane. Let P = {x / x is a line in the plane which is perpendicular to l}.

Illustration
Write H = {Fluorine, Chlorine, Bromine, Iodine, Astatine} in set - builder form.

Solution
H ={x : x is a halogen}

Example 1
Match each of the following sets in the column A described in roster form with the same set in the column B described in the set-builder form.

Column A

Column B

(a) {M, A, T, H, E, I, C, S} (a) {x : x N and x is a multiple of 5}
(b) {5, 10, 15, 20, 25, ...} (b) {x : x R, x x}
(c) {} (c) {x ∠ x is a letter of the word FOLLOW}
(d) {F, L, O, W} (d) {x x is a letter of the word 'MATHEMATICS'}
(e) {1, 2, 3, 4,... 100} (e)
(f) (f) {x : x N and x 100}

Solution
(a) (d)   
(b) (a)      
(c) (b)
(d) (c)
(e) ↔ (f)
(f)  (e) 

Example 2
Write the following sets in set-builder form.
  1. A = {1, 4, 9, 16, 25, ...}
  2. B = {a, e, i, o, u}
  3. C = {2, 4, 8, 16, 32, 64}
  4. {2, 3, 5, 7, 11, 13, 17, 19, 23, ...}
  5. {1, 2, 3, 4,  6, 12, 24, 48}
Solution
  1. A = {x2 ∠ x N}
  2. B = {x : x is a vowel of the English alphabet}
  3. C = {x x > 1 and x is a divisor of 64}
  4. {x  x is a prime number}
  5. {x : x is a divisor of 48}.




Test Your Skills Now!
Take a Quiz now
Reviewer Name