Question

Describe the following sets in set-builder form :

(i) A = {1,2,3,4,5,6}

(ii) B = {1, $\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{4},......$}

Answer 1

(i) In set Builder form, a set is described by some characterizing property p(x) of its elements x.

In this case a set can be described as {x : p(x) hold} or

{x | P(x) holds} which is read as 'the set of all x such that P(x) holds'.

The symbols ':' or 'I' is read as 'such that'.

So, the above set A in Set-Builder form may be written as

$A=XϵN:x<7$

i.e. A is the set of natural numbers x such that x is less than 7.

Or

A ={ $XϵN|\left(\frac{N}{2}\underset{–}{<}x\underset{–}{<}6\right)1\underset{–}{<}x\underset{–}{<}6$ }

i.e. A is the set of natural numbers x such that x is greater than or equal 1 and less than or equal to 6.

(ii) In Set Builder form, a set is described by some characterizing property P (x) of its elements x.

In this case a set can be described as {x : P (x) hold } or

{x | P (x) holds} which is read as 'the set of all x such that P (x) holds'.

The symbols ' : ' or ' I ' is read as 'such that'.

B= {$x:x=\frac{1}{n},nϵN$ }

i.e. B is the set of all those x such that $x=\frac{1}{n}$, where $nϵN$