Class 11 Maths Sets | Set Builder Form |

**Set Builder Form**

In set-builder form, all the elements of a set possess a single common property which is not possessed by any element outside the set.

- In the set {a, e, i, o, u}, all the elements possess a common property, namely, each of them is a vowel in the English alphabet, and no other letter possess this property.

Denoting this set by V, we write V = {x : x is a vowel in English alphabet}.

- Please note that any other symbol like the letters y, z, etc. could be used.
- The symbol should be followed by a colon “
**:**”. - After the sign of colon, we write the characteristic property possessed by the elements of the set and then enclose the whole description within braces.
- If a set of number doesn’t follow any pattern, it can’t be written in set builder form.

More Example of set builder form

- A = {x : x is a natural number and 3 < x < 10} is read as “the set of all x such that x is a natural number and x lies between 3 and 10. Hence, the numbers 4, 5, 6, 7, 8 and 9 are the elements of the set A.

**Numerical**: Write the set {x : x is a positive integer and x < 4} in the roster form.

**Solution**: Since the set has natural numbers less that 4, Set A ={ 1,2,3}

**Numerical**: Write the set A = {1, 4, 9, 16, 25, . . . }in set-builder form.

**Solution**: Number 1, 4, 6, 16, 25.. are squares of natural numbers 1,2, 3,4, 5 etc..

Therefore set ={x : x is a square of N}

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