LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

SET BUILDER FORM

__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.**