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Question

Describe the following sets in set-builder form :

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

(ii) B = {1, 12,13,14,14,......}
(2 Marks)


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Solution

(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=X ϵ N:x<7

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

Or

A ={ X ϵ N| (N2 < x < 6) 1 < x < 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. ______________________________[1 mark]

(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=1n,n ϵ N }

i.e. B is the set of all those x such that x=1n, where n ϵ N

_____________________________[1 mark]


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