LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

SET BUILDER FORM OF RULE METHOD

__Rule Method or Set Builder Form __

**We can represent a set by stating a property that its
elements satisfy. thus the set of natural numbers less than 10 is
=> A = { x / x is a natural number, x < 10 }**

**Or, ****A = { x : x
is a natural number and x < 10 },**

**We read this as ‘A is the set of all elements x such that x
is a natural number and x is less than 10’**

**a) The set ****X = { 2, 4,
6, 8, 10, 12, 14, 16 }**** can be written in the set-builder form as X = { x / x is an even natural number and x ≤ 16 }**

**b) The set of prime numbers that are less than 25 can be
written in the set builder form as ****A = { x / x
is a prime number and x < 25 }**** and the same
set ‘A’ can be written in the tabular form as ****A = { 2, 3, 5, 7, 11, 13, 17, 19, 23 }**

**We sometimes represent a set by describing a property of its
elements inside braces**

**Examples-1)**

**A = { days of a week }, B = { month of the year }, C = {
One digit odd number }, D = { one digit even number }**

**Answer-**

** A = { days of a week }**

** In the tabular form, A = { days of a week }
, **

** A = { Monday,
Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday }**

** B = { month of the year }**

** B = { January, February, March,
April, May, June, July, August, September, October, November, December }**

**
C = { One digit odd number } = { 1, 3, 5, 7, 9 }**

**
D = { one digit even number } = { 2, 4, 6, 8 }**

**Example-2) Set of Prime Number between 10 to 30**

**Ans.) { x / x is prime number, 10 < x < 30 }**

**Example-3) The set of whole numbers which are divisible by 6 and are
less than 40**

**Ans.) { x / x = 6n,
n ∈ W and n < 7 }**

** **

**Example-4) The set of the factors of 50**

**
**

**Ans.) { x / x is a factor of 50 }**** **