SET BUILDER FORM
If the members of a set have a common property then they can be determined by describing the property, for example, the members of the Set Y = { 1, 2, 3, 4 } having a common property, namely all are natural numbers less than 5. No other natural number has this property. So, we can write the set ‘Y’ as follows –
D = { Y / Y is a natural number less than 5 }, which should be read as ‘D’ is the Set of members Y such that Y is a natural numbers less than 5”, that can be precisely written like that – D = { Y / Y ϵ N, Y < 5 }
Sometimes Set D can be written as, D = { Set of all natural numbers less than 5 }. It has been observed that, the description of the common property of the members is given inside the braces { }. This is to be considered as a crude form of the said rule method.
Set builder form can be expressed in the tabular form by listing the objects and satisfying the rule –
Example – a) Z = { Y/ Y is a letter of the word HYDERABAD }
‘Y’ is any of the letters, H, Y, D, E, R, A, B.
So, Z = { H, Y, D, E, R, A, B }
Let, E = { x/x is a whole number greater than 6 but less than 15 }
x is any one of the numbers 7, 8, 9, 10, 11, 12, 13, 14.
So, E = { 7, 8, 9, 10, 11, 12, 13, 14 }.
A set given in the tabular form can be expressed in the set-builder form if the members obey some common property.
Example– 1) Let, Z = { 0, 1, 3, 5, 7 }, Here each of the members is an odd whole number that is less than 8. No other whole number has this property.
So, Z = { x/x is an even whole number less than 8 }
Or, Z = { x/x is one of the first 5 odd whole number less than 8 }
Example- 2) let, A = { 3, -5, c, q, -2, 6 } . Here the members of ‘A’, do not have a common property, so it is difficult to write the Set by the rule method.