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 }