Way of listing the elements of Set

Way of listing the elements of Sets

i)ROSTER METHOD-list all the members or elements of a set

Example 1:The set V of unisza can be written as V = {u,n,i,s,z,a}

Example 2:The set O of even positive integers less than 10 can be expressed by O = {2,4,6,8}

Example 3:The set may consists of elements which have different types with each other, just like: {a, 1, Aiman,Malaysia}

Example 4: Let say there is a set with elements of numbers from 1 to 99. It would be irritating to list out all the elements in the set. Therefore, for a set with fixed pattern of elements, we can use the symbol “…” in the denotion of the set. For example, {1, 2, 3, . . . , 99}.

ii)SET BUILDER-state the properties of the elements. For example, the set O of all even positive integers less than 10 can be written as

O = {x | x is an even positive integer less than 10}

The bold part represents the set builder for the set. As stated in the set builder, x is an even positive integer less than 10. The elements which does not fulfill the properties are not considered as an element of set O. Therefore, the possible elements of set O is { 2, 4, 6, 8 }

The set Q⁺ of all positive rational numbers can be written as

Q⁺ = {x ∈ R | x =p/q , for every integers p and q}

Specify properties of Sets

Sets are inherently unordered:

• No matter what objects a, b, and c denote, fa, b, c g = fa, c, b g = fb, a, c g = fb, c, ag = fc, a, b g = fc, b, ag.

All elements are distinct (unequal); multiple listings make no difference.

• fa, a, b g = fa, b, b g = fa, b g = fa, a, a, a, b, b, b g.
• This set contains at most 2 elements.