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)
(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]